Panoramic camera systems

ABSTRACT

A camera system captures images from a set of cameras to generate binocular panoramic views of an environment. The cameras are oriented in the camera system to maximize the minimum number of cameras viewing a set of randomized test points. To calibrate the system, matching features between images are identified and used to estimate three-dimensional points external to the camera system. Calibration parameters are modified to improve the three-dimensional point estimates. When images are captured, a pipeline generates a depth map for each camera using reprojected views from adjacent cameras and an image pyramid that includes individual pixel depth refinement and filtering between levels of the pyramid. The images may be used generate views of the environment from different perspectives (relative to the image capture location) by generating depth surfaces corresponding to the depth maps and blending the depth surfaces.

CROSS REFERENCE TO RELATED APPLICATIONS

This application claims the benefit of U.S. Provisional Application No.62/485,381, titled “Panoramic Camera Systems” filed Apr. 13, 2017, whichis incorporated by reference in its entirety.

BACKGROUND

Effectively capturing an environment or scene by a set of cameras andrendering that environment to simulate views that differ from theactually-captured locations of the cameras is a challenging exercise.These cameras may be grouped together in a rig to provide various viewsof the environment to permit capture and creation of panoramic imagesand video that may be referred to as “omnidirectional,” “360-degree” or“spherical” content. The capture and recreation of views is particularlychallenging when generating a system to provide simulated stereoscopicviews of the environment. For example, for each eye, a view of theenvironment may be generated as an equirectangular projection mappingviews to horizontal and vertical panoramic space. In the equirectangularprojection, horizontal space represents horizontal rotation (e.g., from0 to 2π) and vertical space represents vertical rotation (e.g., from 0to π, representing a view directly downward to a view directly upward)space for display to a user. To view these images, a user may wear ahead-mounted display on which a portion of the equirectangularprojection for each eye is displayed.

Correctly synthesizing these views from physical cameras to simulatewhat would be viewed by an eye is a difficult problem because of thephysical limitations of the cameras, difference in inter pupillarydistance in users, fixed perspective of the cameras in the rig, and manyother challenges.

The positioning and orientation of cameras is difficult to effectivelydesign, particularly because of various physical differences in cameralenses and to ensure effective coverage of the various directions ofview from the center of the set of cameras. After manufacture of a rigintended to position and orient cameras according to a design, thesecameras may nonetheless be affected by variations in manufacturing andinstallation that cause the actual positioning and orientation ofcameras to differ. The calibration of these cameras with respect to thedesigned positioning and orientation is challenging to solve because ofthe difficulties in determining effective calibration given variousimperfections and variations in the environment in which the calibrationis performed.

When generating render views, each captured camera image may alsoproceed through a pipeline to generate a depth map for the image toeffectively permit generation of synthetic views. These depth mapsshould generate depth in a way that is consistent across overlappingviews of the various cameras and that effectively provides a depthestimate for pixels in the image accurately and efficiently and accountfor changing depth across frames and between objects and backgroundsthat may share similar colors or color schemes. In generating the depthmaps, a large amount of inter-frame and inter-camera data may beprocessed, requiring extensive computational resources.

Finally, in render views, the various overlapping camera views cancreate artifacts when combined, and in some systems create unusualinteractions when two or more cameras depict different colors or objectsin an overlapping area. Resolving this problem in many systems maycreate popping, warping, or other problems in a render view. Inaddition, systems which use a single camera or stitch images togethermay not realistically simulate views for different eyes or at differentlocations.

SUMMARY

An arrangement of a set of cameras considers camera positioning andorientation to optimize or improve field of view coverage for a space,such as a panoramic 360 degree space. The positioning of the cameras isdetermined by evaluating the distance of one or more of the cameras fromone another and adjusting positioning to optimize a scoring function.For a set of camera positions, the orientation of the cameras isoptimized given the fields of view of the cameras to maximize theminimum number of cameras at viewing any given point. Multiple possibleorientations are initialized, and each initialization is solved to findthe configuration of cameras with optimal coverage of a set of testpoints. During application of the solver, the orientations of thecameras are solved with a set of points generated semi-randomly. Toevaluate the solutions of the different initial configuration, thesolutions are evaluated with a set of evenly distributed points.

An image capture system has a set of cameras, each camera having anexpected orientation and position, for example an optimal orientationand position. Since the actual manufacture of the cameras may differfrom a designed or planned orientation, to determine a set ofcalibrations for the cameras, an image is captured from each camera. Theimages are compared to find pairwise feature point matches between theimages. The feature point matches are filtered and analyzed to excludematches that are not consistent with the current camera orientations andpositions or that create high reprojection error compared to othermatches for the image pair. Sets of feature matches are assembled intotraces, which are also filtered and used to calibrate the cameras of theimage capture system with a computational solver, such as a nonlinearsolver. The calibration process may iterate by re-considering initialfeature matches and recalculating feature match consistency,reprojection error, and traces based on the new camera calibrations.

A set of cameras captures images of a scene to be rendered based ondepth information. A pipeline generates a depth map of the images thatcan be parallelized across several processors which may be operating onseparate machines to process different frames. Rendering of each framemay recursively request underlying steps in the pipeline which mayrequire data from other cameras or from other frames forward orbackwards in time from the current frame. For a given frame, as data isgenerated, it is marked as used in the current frame. To reduce memoryrequirements, when beginning a new frame, data cached from the priorframe that was not marked is removed from the cache (and existing markscleared).

Depth maps are generated for pixels of a reference image based onoverlapping images at least partially sharing the field of view of thereference image. An image pyramid of images at various sizes aregenerated for the reference image and the overlapping images. Theoverlapping images are reprojected to the reference camera. At a givenlevel of the image pyramid, the depth map solution for a prior level isupscaled and the pixels in the reference image are sequentiallyevaluated by adopting neighbor pixel depth estimates, if better, andperforming a single step of a gradient descent algorithm. Improvementsin the depth from the single gradient step can propagate throughout thereference image and up the levels of the image pyramid. The refineddepth map may be filtered before upscaling to the next image pyramidlevel. The filters may use a guide to determine a combination ofneighboring pixels for a pixel in an image. In the depth estimates, thefilters may use various edge-aware guides to smooth the depth maps forthe image and may use prior frames, color, and other characteristics forthe guide.

A set of filters blurs a depth map for an image based on amachine-learned set of image transforms on the image. The imagetransforms are applied to the image to generate a guide for filteringthe depth map. The parameters for the image transforms are learned froma set of images each having a known depth map. To train the parameters,the known depth map for an image is randomly perturbed to generate adepth map to be improved by the filter. The parameters for thetransforms are then trained to improve the correspondence of an outputdepth map to the original depth map when the transformed image guidesthe filtering.

A view of a scene can be rendered from a set of images withcorresponding depth maps. Each image with a depth map can be rendered asa “depth surface” with respect to the desired view. The depth surfacesfrom each image can be added and blended based on alpha channelsassociated with each image. To render an image with an equirectangularprojection, each depth surface triangle can be selectively shifted tocorrect for the equirectangular projection.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 illustrates an example image capture system, according to oneembodiment.

FIG. 2 illustrates the useable image area of a camera sensor, accordingto one embodiment.

FIG. 3A illustrates the estimated coverage area of an image, accordingto one embodiment.

FIG. 3B is a graph illustrating an example camera coverage function fora camera, according to one embodiment.

FIG. 4A illustrates an example randomized set of test points, accordingto one embodiment.

FIG. 4B illustrates an example evenly distributed set of test points,according to one embodiment.

FIG. 5 is a graph illustrating an example coverage scoring function,according to one embodiment.

FIG. 6 is a flowchart illustrating an example process for selectingcamera position and orientation according to one embodiment.

FIG. 7 is a block diagram illustrating an example computing environmentin which an image capture system operates.

FIG. 8 is a flowchart illustrating an example process for capturing andusing content in an image capture system, according to one embodiment.

FIG. 9 is a flowchart illustrating an example process for storing andrendering image capture system content, according to one embodiment.

FIG. 10A illustrates example memory management state, according to oneembodiment.

FIG. 10B illustrates a second example memory management state, accordingto one embodiment.

FIG. 11 is a block diagram illustrating an example computing environmentin which in which an image capture system is calibrated, according toone embodiment.

FIG. 12 illustrates an example scene captured from two overlappingcameras of an image capture system, according to one embodiment.

FIG. 13A illustrates example matched feature points between two imagesof an example scene, according to one embodiment.

FIG. 13B illustrates an example list of matching feature points,according to one embodiment.

FIG. 14A illustrates an example triangulation based on two triangulationrays, according to one embodiment.

FIG. 14B illustrates an example triangulation based on multipletriangulation rays, according to one embodiment.

FIGS. 15A and 15B illustrate example reprojections and reprojectionerrors between feature points and reprojected points, according to oneembodiment.

FIG. 16 is a graph illustrating an example trace, according to oneembodiment.

FIG. 17 is a flowchart illustrating an example process for calibratingan image capture system, according to one embodiment.

FIG. 18 is a flowchart illustrating an example calibration process foriteratively improving the calibration of an image capture system,according to one embodiment.

FIG. 19 illustrates an example image pyramid, according to oneembodiment.

FIG. 20 illustrates an example reprojection of overlap images to areference image, according to one embodiment.

FIG. 21A illustrates an example order to refine the depth estimation ofpixels of an image, according to one embodiment.

FIG. 21B illustrates an example pixel with proposals from neighboringpixels, according to one embodiment.

FIG. 22A illustrates an example reference image with a reprojectedoverlap image overlaid, according to one embodiment.

FIG. 22B illustrates an example reference image with an applied depthmap, according to one embodiment.

FIG. 23 is a flowchart illustrating an example process for determining adepth estimate for a set of images based on an image pyramid.

FIG. 24 is a flowchart illustrating an example process for refining thedepth estimate of an image, according to one embodiment.

FIG. 25 is a flowchart illustrating an example process for maintainingconsistency between depth estimates, according to one embodiment.

FIG. 26 illustrates an example process for filtering a depth map basedon a guide, according to one embodiment.

FIG. 27A illustrates an example process for training a set of transformsto filter a depth estimate, according to one embodiment.

FIG. 27B illustrates an example process for using a set of transforms tofilter a depth estimate, according to one embodiment.

FIG. 28 illustrates an example environment in which a scene is renderedfrom a set of depth surfaces.

FIG. 29 is an illustration of a render view comprising a rendered depthsurface, according to one embodiment.

FIG. 30 is an illustration of a render view comprising a set of blendedrendered depth surfaces, according to one embodiment.

FIG. 31A illustrates an example depth surface with discontinuitiesaround an obstructing object, according to one embodiment.

FIG. 31B illustrates an example depth surface with discontinuitycorrection, according to one embodiment.

FIG. 31C illustrates an example sectioned depth surface, according toone embodiment.

FIG. 32A illustrates an example situation in which a sectioned depthsurface is rendered from a different angle, according to one embodiment.

FIG. 32B illustrates an example situation in which an extended sectioneddepth surface is rendered from a different angle, according to oneembodiment.

FIG. 33 illustrates rendering a triangle for a render view using anequirectangular projection, according to one embodiment.

FIG. 34 is a flowchart outlining an example process for generating arender view based on a set of depth surfaces, according to oneembodiment.

The figures depict various embodiments of the present invention forpurposes of illustration only. One skilled in the art will readilyrecognize from the following discussion that alternative embodiments ofthe structures and methods illustrated herein may be employed withoutdeparting from the principles of the invention described herein.

DETAILED DESCRIPTION

System Architecture and Design

To effectively capture images of an environment for rendering views, animage capture system obtains images from a number of cameras that arepositioned and oriented to increase the number of cameras having a viewof any particular location in the environment. That is, an image capturesystem may be designed to increase the minimum number of cameras thatmay capture information about any given environment around the imagecapture system.

FIG. 1 illustrates an example image capture system, according to oneembodiment. An image capture system can be used to, for example, capturemultiple images of a scene (for example, a physical environment in whichan image capture system is located) from different viewpoints (from eachcamera's position) that can be processed to be later presented to a uservia a head mounted display or other stereoscopic viewing display, and insome cases for presentation on a monoscopic display or other suitablesystem. For example, the captured images from an image capture system100 can be used to generate a virtual reality version of a scene, torender a 360 degree images of a scene from one or more points of view,or to generate any other suitable view of a scene. Image contentcaptured by an image capture system 100 can be associated into imagesets comprising a simultaneously (or substantially simultaneously)captured image or video frame from each camera of the image capturesystem 100. In some embodiments, the images captured by the imagecapture system 100 captures images of the environment in a fullpanoramic, 360-degree view of the scene in which it is located. Theimage capture system 100 of FIG. 1 includes a plurality of cameras 110mounted to the image capture system body 115 of the image capturesystem. Each camera captures a field of view (“FOV”) representing theportion of the environment captured by the sensor of the camera. Byanalyzing the images from each camera, panoramic views of theenvironment may be generated for the environment.

Each camera 110 can be a still or video camera capable of capturingimage data about the scene through an image sensor of the camera. Eachcamera 110 can have a defined or variable angle of view (“AOV”), forexample based on a lens of the camera 110. An angle of view representsthe angle through which the lens of a camera 110 can direct light intothe image sensor of the camera 110 capture image data, thereforedetermining how wide or narrow the field of view of the camera 110 is.For example a camera 110 can have a wide angle lens with a high AOV (forexample a fisheye lens), alternatively a camera can have a telephotolens with a comparatively low AOV. In some embodiments, each camera 110is similar or identical, for example having an identical focal length toeach other camera 110. In other embodiments, different cameras 110 canvary, comprising different lenses, sensors, or focal lengths from othercameras 110 of the image capture system 100, for example a camerapointed vertically can be distinct from the other cameras 110 of theimage capture system 100. In some embodiments, the cameras of the imagecapture system 100 are globally synchronized to capture images and/orvideo at the same time, for example using a global shutter to improveperformance for capturing fast moving objects. The cameras 110,according to the embodiment of FIG. 1, are supported and positioned bythe image capture system body 115.

When designing an image capture system 100 the position and orientationof the cameras 110 can be determined to maximize the field of viewcoverage of the environment by the cameras 110. The positioning of thecameras in the image capture system body 115 describes the location of acameras with respect to the image capture system body 115, while anorientation of a camera describes the rotation of the camera and affectsthe portion of the environment viewed by the camera. Similarly, the lenscharacteristics of a camera can describe the AOV of the camera,centering of the lens on the image sensor, and the distance of the lensplane from the image sensor of the camera 110. A “camera configuration”can collectively describe the position, orientation, and lenscharacteristics of a camera 110, enabling the determination of the FOVof the camera. Similarly, the configuration of the image capture systemincludes configurations for each camera 110.

According to some embodiments, optimal camera positions for the imagecapture system 100 are determined to “evenly” distribute the cameras inthe image camera system body 115. This positioning may be determined bymodeling the positions of the cameras as having a cost or “energy”reflecting the closeness of the cameras to one another. For a cameraclose to other cameras, this camera may have a relatively high cost orenergy, suggesting the camera should be moved to reduce the energy. Insome implementations, camera positions for the image capture system 100are determined by modeling each camera in a Thomson problem for thesystem. The Thomson problem can be solved to determine the optimalpositioning of a given number of cameras 110 around a spherical body.The Thomson problem can be solved by assigning each camera 110 an energyinversely proportional to the pairwise distances between that camera 110and each other camera 110 in the image capture system 100. Then theenergy of the entire system can be minimized (for example, iterativelyusing a non-linear solver), resulting in the optimal camera positionsfor the image capture system 100. Then, the camera orientations can bedetermined to maximize the image coverage of the surroundingenvironment.

FIG. 2 illustrates the useable image area of a camera sensor, accordingto one embodiment. The environment of FIG. 2 comprises an image sensor210 of a camera 110, a lens image 220 projected on the image sensor 210by light passing through the lens, and a corresponding useable imagearea 230 of the image sensor 210 where the lens image 220 intersectswith the image sensor 210. In some embodiments, a lens of a camera 110casts a lens image onto the image sensor 210, allowing the image sensor210 to capture images for use in the image capture system 100.

An image sensor 210 captures light on a series of pixels of the imagesensor 210 in a raw image format from which an image can be generated.For example, the image sensor 210 of FIG. 2 comprises a rectangular gridof pixels able to capture light from a lens image 220 projected onto theimage sensor 210. In some implementations the lens image 220 projectedby a lens of a camera 110 does not precisely align with the image sensor210. The area of the image sensor 210 on which the lens image 220 isprojected can be referred to as the useable image area 230. However, insome embodiments, such as the embodiment of FIG. 2, the useable imagearea 230 does not extend to the entire image sensor 210. Therefore, somepixels of the image sensor 210 outside of the useable image area 230 donot carry useful image data. In some embodiments, the raw image iscropped to remove unusable sections of image, but in other embodiments,the full raw image can be used. Similarly, a lens image 220 can exhibitprogressive distortion near its edges (for example caused by limitationsin the design or manufacture of the lens itself), and therefore thequality and usability of the raw image data captured by the image sensor210 can degrade towards the edges of the image sensor 210 and lens image220.

When determining the field of view (and therefore coverage area) of agiven camera 110 (for example based on the camera configuration of thecamera 110), the degradation of image quality and therefore coveragetowards the edges of the raw images captured from the image sensor canbe accounted for by applying an image coverage gradient to an expectedcaptured image. Even where the image quality does not degrade, or doesnot degrade significantly, an image coverage gradient may be applied topermit orientation of the camera to partially effect calculated coverageof a pixel. As discussed below, this may improve differentiation of thecoverage function for a camera and improve a solver (e.g., a non-linearsolver) calculating how changes in orientation affect the view of pointsin the environment.

FIG. 3A illustrates the estimated coverage area of an image, accordingto one embodiment. The example captured image 310 of FIG. 3A comprisesfull coverage area 320 which slowly degrades through a partial coveragearea 325 to a no coverage area 330. According to some embodiments, theestimated coverage of a captured image 310 can be set to reflect the(typically) degrading quality of the image towards the edges of thecaptured image 310. Similarly, FIG. 3B is a graph illustrating anexample camera coverage function for a camera, according to oneembodiment. The graph of camera coverage function 350 of FIG. 3Bcomprises a full coverage area 320 which slowly tapers off towards theedges of the frame. In some implementations, a sigmoid curve is used tomodel the camera coverage function for a camera 110 of the image capturesystem 100.

To compare different possible camera orientations, a coverage scoringfunction can be generated to score camera orientation configurations,where a camera orientation configuration comprises the orientation ofeach camera 110 of the image capture system 100. A coverage scoringfunction is a measure of the camera coverage of the environment by animage capture system with a given configuration. According to someembodiments, the field of view (that is, the portion of a scene thatwould be visible in an image captured from a camera 110) for each camera110 of the image capture system 100 can be estimated from the cameraorientation configuration. This field of view may be determined withrespect to a set of test points in the environment, which may be evenlydistributed or generated to have some random perturbations. The testpoints having random perturbations may be generated randomly orsemi-randomly as discussed below.

To calculate the coverage scoring function for a given cameraorientation configuration, the configuration can be evaluated withrespect to the set of test points and scored based on the amount andquality of coverage of the test points of the set. Based on the resultsof the coverage scoring function, the camera orientation configurationcan be iteratively adjusted until an optimal camera orientationconfiguration is determined from the prior camera orientationconfiguration.

FIG. 4A illustrates an example randomized set of test points, accordingto one embodiment. In some implementations, a random or semi-random setof test points is employed to avoid iterative improvements overfittingthe camera configuration to the specific set of test points. The set ofrandomized test points can be re-generated between iterations to avoidoverfitting, according to some embodiments. The test point set 400 ofFIG. 4A comprises a plurality of test points 410 distributed around aspherical shell. In some embodiments, each test point set 400 comprisesapproximately 3000 test points 410. To generate a set of semi-randomtest points, first a set of random points are generated. Each test point410 is assigned an energy based on its proximity to other test points.For example, the energy of each test point in one embodiment isinversely proportional to the distance from that test point to nearbytest points. The highest energy test points, that is, the test pointsmost closely clustered with its neighbors can then be eliminated andreplaced with new random test points until the maximum energy of anytest point 410 is reduced below a threshold level, or based on any othersuitable criteria being met. In one example, several test points areeliminated at once, for example test points that exceed the thresholdlevel.

FIG. 4B illustrates an example evenly distributed set of test points,according to one embodiment. A spherical Fibonacci lattice distribution(or Fibonacci spiral distribution) is an example of anevenly-distributed set of test points. The Fibonacci lattice set 450 ofFIG. 4B comprises a plurality of Fibonacci lattice points evenlydistributed in a Fibonacci lattice. In some embodiments, theevenly-distributed test points, such as a Fibonacci lattice set, is usedin an evaluation of a camera orientation configuration. In otherembodiments, various other mathematically-generated orevenly-distributed points are used.

FIG. 5 is a graph illustrating an example coverage scoring function fora given set of test points, according to one embodiment. The graph 500of FIG. 5 plots an example coverage scoring function 520 score 505 overdifferent possible camera configuration 510. The coverage scoringfunction has a plurality of local maxima 530 and is a complicated,possibly nonlinear function. The graph 500 is an abstraction of ageneral coverage scoring function representing orientationconfigurations of the cameras 110 in a large number of various possibleorientations. Thus, in some embodiments, a similar graph to accuratelyrepresent the degrees of freedom of the configurations would includemany more dimensions, or be otherwise difficult to generate.

In some embodiments, the coverage scoring function 520 is determined tomeasure and maximize the minimum coverage of cameras for any given testpoint. That is, for the test points, the coverage scoring function 520may measure the minimum number of cameras viewing any given test point.For a given camera orientation configuration and test point set, eachtest point of the test point set can be evaluated for coverage bydetermining if that test point would be visible in an estimated imagefrom each camera 110 and where in the estimated captured image 310 thattest point would fall (i.e. the estimated coverage 350 of that point inthe image ranging from 1-0), according to some implementations. Thecamera coverage functions 350 as shown in FIG. 3 and discussed above maythus be used to score the value of the view of a test point from a givencamera, and may prefer a view of a test point that is more central to acamera. In addition, the camera coverage function 350 may improve theability of a nonlinear solver (or other suitable solving method) toevaluate and improve the camera orientations by providing differentiablecoverage functions for the test points with respect to changes in cameraorientation.

In some embodiments, the estimated coverage for each camera for a testpoint can be summed, resulting in a coverage number for each test pointrepresenting the number of cameras 110 in which the test point is in thecamera's FOV. In some implementations, the coverage number is thenrounded down to the nearest integer and the minimum coverage number inthe test point set is selected as the result of the coverage scoringfunction for the test point set, though the coverage numbers can also beaveraged or otherwise weighted according to other embodiments. In someembodiments, a decimal is appended to the rounded coverage numbers toprovide a secondary score representing the percentage of test pointshaving greater than the minimum coverage number. For example, a coveragescoring function of 3.75 can represent a minimum coverage of 3, i.e. atleast 3 cameras 110 can see any given test point, with 75% of testpoints having a coverage greater than 3. The second score may alsoimprove performance of the nonlinear solver (or other suitable iterativeoptimization method) by providing a means to evaluate an orientation'spartial coverage towards the next highest number of minimum camerasviewing all test points.

According to some implementations, multiple camera orientationconfigurations are simultaneously generated and iteratively improved, asthe coverage scoring function 520 for a given system can generally beassumed to have multiple local maxima 530. Starting with severaldisparate (for example, randomly generated) camera orientationconfigurations can allow the optimization process to be optimize cameraorientation configurations to different local maxima 530 of the coveragescoring function 520, out of which the most efficient camera orientationconfiguration can be chosen (that is, the configuration at the “best”local maxima). To optimize the coverage scoring function for a giveninitialization, any suitable method, for example a nonlinear solver, canbe used. Thus, in this example the nonlinear solver may optimize theorientation configuration of the cameras jointly using the cameracoverage function 350 reflecting the quality (or centrality) of thecoverage of a test point for a camera 110 and to optimize the scoringfunction that maximizes the minimum number of cameras viewing the testpoints (e.g., the coverage scoring function 520).

FIG. 6 is a flowchart illustrating an example process for selectingcamera position and orientation according to one embodiment. The process600 begins by determining 610 camera positions to optimize the distancebetween cameras, for example by solving the Thomson problem for thedesired number of cameras in the image capture system. Then, a set oftest points are generated 620 against which to evaluate the coverage ofthe camera orientation configuration. For example, the test points canbe generated semi-randomly, randomly, or optimally (for example, using aFibonacci lattice set). Next, a set of camera orientation configurationare initialized (generated 630) and scored 640 with respect to thegenerated test point set. For example, each camera orientationconfiguration can be evaluated based on a coverage scoring functionaccounting for the minimum number of cameras in which any given testpoint will be visible in. The configurations are optimized 650 toimprove the scoring for each camera orientation configuration, forexample, based on the coverage scoring function. This optimization mayuse a nonlinear solver as discussed above. Once each configuration isoptimized 660, the final camera orientation configurations are evaluated670 using the coverage scoring function based on an evenly-distributedtest point set, such as a Fibonacci lattice set. The highest-scoringcamera orientation configuration can then be selected 680 based on theevenly-distributed test point set and used to design and manufacture theimage capture system 100. Based on the determined camera positions andorientations, the image capture system 100 can be manufactured.

Image Processing System Overview

When cameras are positioned and oriented, the camera system may captureimages for use in rendering views of an environment. To do so, thecamera system may calibrate the manufactured cameras, process imagescaptured from the cameras, determine depth maps associated with thecaptured images, and use the depth maps in rendering views of theenvironment.

A depth map describes the estimated depth of the pixels in an image. Incaptured images, there may be many different objects at differentlocations in the image, such as nearby objects, distant objects, andobjects in between. The depth map may specify a depth for eachindividual pixel of the image, or may provide a depth estimate forgroups or blocks of pixels in the image (for example, when the depth mapis lower resolution than the associated image). Typically, depth may bestored inversely to the depth distance, such that distances in the fardistance (approaching infinity) are stored as values approaching 0. Forexample, the depth may be stored as 1/d, such that a distance of 50 m isstored as 1/50 or 0.02, and a distance of 1 km is stored as 1/1000. Thisprovides a large range of values for close depths which may be moreimportant to distinguish.

FIG. 7 is a block diagram illustrating an example computing environmentin which an image capture system operates. The environment of FIG. 7comprises an image capture system 100 and an image processing system 710connected by a network 720.

The image capture system 100 can be any suitable image capture systemcapable of capturing images of a scene to be processed and combined.According to some embodiments, the image capture system 100 is connectedto an image processing system over the network 720, and can receiveinstructions (for example, instructions to capture or transmitpreviously captured images), and transmit information (such as raw orprocessed image data and/or metadata) to the image processing system 710over the network 720. For example, as described above, an image capturesystem 100 can be used to, for example, capture images to render aversion of a captured scene, or to render a 360 degree image of a scene.In other embodiments, the image capture system 100 can be any suitablesystem to capture images of a scene.

The network 720 can be any suitable network or communication method. Forexample, the network 720 can be any suitable wired or network, and canbe a local area network (LAN), wide area network (WAN), the Internet, orany other suitable network.

In the embodiment of FIG. 7, the image processing system 710 can be anysuitable computing device capable of receiving and processing image datafrom the image capture system 100. For example, the image processingsystem 710 can be a laptop, desktop, mobile device, server, servergroup, or other suitable computing device. The image processing system710 receives captured images from the image capture system 100,processes the received images, calculate depth maps for the processedimages, and render output images from specific viewpoints to representthe scene based on the received images and the calculated depth maps(herein, a viewpoint represents a specific field of view, position,position and orientation of a camera or rendered image). For example, afinal image can be any image depicting a scene so that the scene can berecreated in virtual reality or otherwise displayed to the user, forexample a panoramic, spherical panoramic, or suitably wide angle imagedesigned to be viewed through a head mounted display. The output imagecan be in cubemap, equirectangular, or cylindrical formats inresolutions such as “8K” (for example 8192 by 8192 pixels). In addition,multiple views may be generated, such that one view is generated foreach display corresponding to each eye of the user.

In the embodiment of FIG. 7, the image processing system 710 comprises acalibration module 712, processing module 714, depth calculation module716, and rendering module 718. In some embodiments, the image processingsystem 710 or certain functionality of the image processing system 710is integrated into the image capture system 100.

The calibration module 712 determines the position and orientation ofthe cameras 110 of the image capture system 100 to calibrate the actualposition and orientation of the cameras as-manufactured compared to theintended positon and orientation of the cameras as designed. Thefunctionality of the calibration module 712 is discussed further below.Based on the calibration, the processing module 714 processes raw imagesreceived from the image capture system 100 to prepare the images fordepth map calculation. For example, the processing module 714 canprocess raw image data received from the image capture system 100 into aprocessed and filtered RGB image (such as using a joint bilateral filterto reduce noise in the image). The depth calculation module 716 receivesan image set of simultaneously captured images or synchronized video andcalculate a depth map for each image of the image set or frame of video.The depth calculation module 716 is discussed in further detail below.

Finally, the rendering module 718 renders image sets or synchronizedvideo (in some implementations with associated depth maps) into outputimages and or video for a user to view. The process for rendering anoutput image is discussed further below. In some implementations, thefunctionality of the rendering module 718 can be performed in real timeor substantially in real time, and/or at a client device (such as at ahead mounted display rendering the view) separate from the imageprocessing system 110.

FIG. 8 is a flowchart illustrating an example process for capturing andusing content in an image capture system, according to one embodiment.The process of FIG. 8 begins after calibration of the image capturesystem, for example, as described below. The image capture systemcaptures raw image content from the surrounding environment and sendsthe raw image content to the image processing system, where it isreceived 810 and stored. For example, the raw image content can be inthe form of image sets in a raw image format (i.e. unprocessed orminimally processed data from the image sensors of the cameras 110 ofthe image capture system 100). The raw image content is then filtered820 at the image processing system, for example for de-noising purposes,by a median filter, weighted median filter, bilateral filter, jointbilateral filter, or any other suitable edge aware filter. For example,image content and/or depth maps can be filtered using a joint bilateralfilter with any suitable guide image. Similarly, one or more of thefilters may have a time dependency, for example a joint bilateral filterwith a 3D kernel requiring image data from adjacent frames of the imagecontent. Then the image processing system converts 830 the filtered rawimage content into standard image content. For example, standard imagecontent can be a RGB raster image in a standard compressed oruncompressed image format, such as bmp, png, tiff, or any other suitableformat. Next, the standard image content 840 is filtered, for examplefor de-noising purposes, by any suitable filter, and depth maps aregenerated 850 for each image of the standard image content. The processfor generating a depth map based on image content is discussed in detailbelow. The generated depth maps can then be filtered 860, for examplefor de-noising purposes or to maintain the consistency of depth mapsacross multiple images. Finally, final image content is rendered 870based on the depth maps and the processed image content. The process forrendering final image content will be discussed in greater detail below.

In some embodiments, the image processing system 710 processes andmanages a large amount of data, including uncompressed raw image data,and stores the data in memory to be able to efficiently generate andfilter depth maps and/or render final image content. Therefore, in someimplementations, the image processing system 710 uses a “mark and sweep”system of memory management when processing and storing image contentfrom the image capture system 100. For example, mark and sweep methodscan be used when depth maps for many successive frames (each with anassociated image set from the image capture system 100) need to begenerated sequentially or when filters with a large time dependency(requiring image data from many successive frames) are used.

FIG. 9 is a flowchart illustrating an example process for storing andrendering image capture system content, according to one embodiment. Theprocess of FIG. 9 begins when a frame is selected for a depth mapcalculation 910, for example, the first frame of a video clip capturedby the image capture system to be rendered. Then, the image processingsystem 710 checks for components required for the depth calculation andmakes a recursive call 920 to retrieve the end product of the depthcalculation (for example, the filtered depth map). If the subject of therecursive call is not found, the process generates the subject, issuingfurther recursive calls for any component parts of the subject. Forexample, if the filtered depth map is not found, a recursive call isissued for the depth map, and when the depth map is returned, thefiltered depth map is generated. Similarly, if the depth map is notfound, recursive calls can be issued for the filtered images fromseveral previous and future frames to generate the depth maps for thecurrent frame (the additional time dependency may be cause bytime-dependent filters used to generate the depth maps 1050). In someimplementations, each recursive call “marks” or flags 930 any of thecalculated components stored in memory. Other implementations mark 930used components after the depth calculation (for example based on thecurrent frame or any other suitable criteria). Finally, any unmarked(i.e. unused) components still stored in memory are “swept” or deleted940 from memory and marks are reset. The process continues for the nextframe in sequence if all frames are not completed 950. In someimplementations, depth map calculations for a sequence of frames can besplit between multiple image processing systems 710. To ensure temporalconsistency between depth estimates calculated between the differentimage processing systems 710, information about additional buffer framesbased on the total time dependency of the pipeline are required (thatis, if an image processing system were to calculate the frames 0-50 of asequence using a pipeline with a time dependency of 5, the imageprocessing system may receive and use information for the frames 0-55 tocalculate the needed section). In some embodiments, depth maps arecalculated for the buffer frames (and potentially discarded), but inother embodiments information for the buffer frames is received and usedat the image processing system 710 without calculating a depth map forthe buffer frames.

FIG. 10A illustrates example memory management state, according to oneembodiment. The environment 1000 of FIG. 10A shows the state of memoryafter the calculation of a filtered depth map 1060 for frame 4. In thestate 1000 the filtered depth map 1060 for frame 4, the depth map 1050for frame 4, the filtered images 1040 for frames 4-6, etc. were requiredto calculate the filtered depth map 1060 and are therefore marked.During the following sweep step, each component stored in memory isfound to be marked, and therefore all components stored in memory areretained, albeit with no marks. For example each recursive call canoperate based on a similar process; a recursive call may first determinea set of precursor components needed to generate the subject componentand check to if each precursor component is already in memory. Anyprecursor components already in memory are marked, and additionalrecursive calls are made to generate or retrieve any missing components.Then the subject of the recursive call can be generated based on theprecursor components, and the recursive call returns (for example, to aparent recursive call).

Moving to the next frame of calculation, FIG. 10B illustrates a secondexample memory management state, according to one embodiment. Theenvironment 1005 of FIG. 10B shows the state of memory after thecalculation of a filtered depth map 1060 for frame 5 (immediately afterthe calculation of the filtered depth map for frame 4 as depicted inFIG. 10A). In the new state 1005 the filtered depth map 1060 for frame5, the depth map 1050 for frame 5, the filtered images 1040 for frames5-7, etc. were required to calculate the filtered depth map 1060 for thenew frame 5 and are therefore marked by virtue of that use. However, inthis state 1005 several components used in the calculation for frame 4were unused and remain unmarked, for example the filtered raw images1020 for frame 2. During the following sweep step, each unmarkedcomponent stored in memory is removed from memory (though, in someembodiments, retained in long term storage) and the remaining (marked)components stored are retained in memory, albeit with no marks. In otherembodiments, any suitable marking scheme can be used.

Image Capture System Calibration

Calibrating an image capture system 100 refers to determining the actualphysical positions, orientations, and lens characteristics of thecameras 110 of a physical image capture system 100. ISE calibration isbased on the expected configuration of the ICS as it was designed.However, in some implementations, small differences between imagecapture systems 100 (for example, due to manufacturing tolerances) meanthat calibration is necessary to determine the correct positions andorientations of the cameras 110.

FIG. 11 is a block diagram illustrating an example computing environmentin which in which an image capture system is calibrated, according toone embodiment. The environment 1100 FIG. 11 comprises an image capturesystem 100 capable of capturing images, a calibration device 1110 tocalibrate the image capture system 100, and a network 1120 connectingthe calibration device 1110 to the image capture system 100. The imagecapture system 100 can be any suitable image capture system comprisingmultiple cameras with an expected position and/or orientation. Forexample, the image capture system 100 can be an image capture systemsuch as the image capture system illustrated in FIG. 1 and associateddescription. The network 1120 can be any suitable network, for examplethe network 720 described above. According to some embodiments, thecalibration system 1110 can be any suitable device, for example an imageprocessing system 710 comprising a calibration module 712, or a separatesuitable computing device. Thus, the calibration performed by thecalibration device 1110 may also or alternatively be performed by thecalibration module 712 of the image processing system 710.

According to some embodiments, calibration of the image capture system100 can occur based on a calibration set comprising single calibrationimages captured simultaneously from each camera 110 of the image capturesystem 100, for example of a scene in which the image capture system 100is located. Using the calibration set and an initial calibration derivedfrom the expected (but not necessary actual) position and orientation ofeach camera 110 the calibration device 1110 can determine the actualposition and orientation of each camera 110 in the image capture system100 and describe the position and orientation of the cameras using a setof calibration parameters for the cameras. FIG. 12 illustrates anexample scene captured from two overlapping cameras of an image capturesystem, according to one embodiment. The environment of FIG. 12comprises two cameras 1210 and 1220 with an overlapping field of view1230 and calibration images 1212 and 1222 captured from the cameras witha corresponding overlapping area 1232. For example, the expected overlapbetween two cameras 1210 and 1220 can be determined based on the fieldof view of the two cameras according to the current calibration. In someembodiments, each of the cameras 1210 and 1220 are cameras of the imagecapture system 100 and are oriented such that the field of view ofcamera 1 1210 overlaps 1230 with the field of view of camera 2 1220;i.e. an object can be positioned in a scene such that the object will becaptured in simultaneously captured images from both camera 1 1210 andcamera 2 1220. Similarly, the calibration images 1212 and 1222 can besimultaneously captured calibration images from camera 1 1210 and camera2 1220, respectively. In some embodiments, the expected overlapping area1232 can correspond to the overlapping field of view 1230 of the cameras1210 and 1220.

To calibrate an image capture system based 100 on a calibration set thecalibration device 1110 can first attempt to identify objects visible inmultiple images of the calibration set by identifying and matchingfeature points in common between images. FIG. 13A illustrates examplematched feature points between two images of an example scene, accordingto one embodiment. The environment 1300 of FIG. 13A comprisescalibration images 1310 and 1320 expected to overlap at the expectedoverlapping area 1340, where each calibration image 1310 and 1320 isassociated with a set of feature points, 1312-1318 and 1322-1328respectively, and a set of feature matches 1332-1338.

Initial identification of matching feature points across the images ofthe calibration set can occur by any suitable method. According to someimplementations, a feature matching algorithm, for example COLMAP, ORB,or any another suitable feature matching algorithm, can be used togenerate an initial feature set. In some implementations, for exampleimplementations using COLMAP to generate the initial feature set,initial feature identification operates over the entire calibration set,independent of the current calibration of the image capture system 100.For example, the feature matching algorithm can determine and return aset of pairwise features (that is, features matching between two imagesof the calibration set), even for calibration images associated withcameras not expected to overlap based on the expected calibration of theimage capture system 100. Initial feature identification can return anumbered list of features (each associated with a coordinate point inthe calibration image) for each calibration image of the calibration setas well as a list of feature matches between images of the calibrationset. FIG. 13B illustrates an example list of matching feature points,according to one embodiment. The table 1350 of FIG. 13B comprisesfeature matches between the feature points 1312 and 1322, 1314 and 1324,1316 and 1326, and 1318 and 1328.

According to some implementations, the initial feature set can comprisemany false positive (or seemingly false positive) features, for examplematching features between calibration images not expected to overlapbased on the initial calibration or matching features in regions ofcalibration images not expected to overlap, even if other areas of thosecalibration images are expected to overlap. Therefore, each initialfeature match can be compared to the expected overlapping areas of eachcalibration image. If the initial feature match falls outside of anappropriate overlapping area, that feature match can be discarded. Asdiscussed above, expected overlap can be calculated based on the currentcalibration information of the image capture system 100 (for examplebased on current knowledge of the position, orientation, and lenscharacteristics of each camera 110). For example, an initial featurematch between the calibration image 1310 and the calibration image 1320of FIG. 13A would be discarded if either feature of the match wasoutside of the expected overlapping area 1340. Based on currentknowledge of the image capture system 100 calibration, this step canreduce false positive matches. Thus, the set of feature matches afterremoving “impossible” matches can be determined (hereinafter, the“possible match set”).

Next, each remaining feature match of the possible match set can betriangulated to associate the feature match with a specific position in3D space. For example, a feature match can be triangulated bycalculating an estimated point in 3D space based on the location of thefeature point in the view and the location of calibration of the camerasin which the point appears. For example, the 3D point may betriangulated from rays originating at the camera in a direction based onthe camera calibration and the position of the feature in the image.FIG. 14A illustrates an example triangulation based on two triangulationrays, according to one embodiment. The environment 1400 of FIG. 14Acomprises two triangulation rays 1405 originating from the 3D rayorigins 1410 which are estimated to pass in close proximity at theclosest points 1415, resulting in the estimated 3D feature location at1420. FIG. 14B illustrates an example triangulation based on multipletriangulation rays, according to one embodiment and is discussed furtherbelow.

To triangulate a feature match, first a triangulation ray 1405 iscalculated for each feature in the feature match. For example, thefeature points 1318 in calibration image 1310 and 1328 in calibrationimage 1320 are matched in the example of FIG. 13. Therefore, atriangulation ray 1405 is calculated for each of the feature points 1318and 1328. The origin point 1410 of each triangulation ray 1410 iscalculated based on the position (i.e. the known position according tothe current calibration of the image capture system 100) of theassociated camera 110. For example the 3D ray origin of thetriangulation ray 1405 associated with the feature point 1318 can bebased on the position of camera 1 1210 (camera 1 1210 is assumed to havecaptured the calibration image 1 1310). In some implementations the 3Dray origin is simply set to an origin point of the appropriate camera,but embodiments can also take into account the position on the imagesensor where the pixel associated with the feature point is located.

After the ray origin 1410 is determined, the direction of eachtriangulation ray can be determined based on the location of the featurepoint within the calibration image. Each pixel in a calibration imagecaptured by a camera 110 can represent a ray of light passing throughthe lens of the camera 110 and striking the image sensor of the camera110 in a location corresponding to that pixel. Based on knowninformation about the camera 110 (i.e. the known position, orientation,and lens characteristics of the camera 110 according to the currentcalibration of the image capture system 100) this ray can be calculatedand reversed to become a triangulation ray pointing from the relevantimage sensor location towards the point in 3D space assumed to havegenerated that ray.

Once the triangulation rays 1405 corresponding to each feature point ofthe feature map are calculated the points can be triangulated. Ideally,all the triangulation rays 1405 for the feature map would intersect atthe precise 3D location of the feature 1420, in practice, however, thisis unlikely to occur even if the feature match does represent anaccurate match for the same feature visible across multiple calibrationimages. For example, rounding error, errors in the calibration of theimage capture system 100 (for example, an error in the actualorientation of a camera 110 can skew the direction of a triangulationray 1405 associated with that camera), or other minor errors causetriangulation rays 1405 not to perfectly intersect. In addition thefeature match may not be a true match, i.e. the feature match can bebetween similar-looking areas of separate objects (for example a matchbetween two distinct but similar looking blades of grass) or due to abug or oversight in the generation of the initial feature set.Therefore, the “closest” location between the triangulation rays 1405can be calculated to determine the estimated 3D feature location 1420.In some embodiments the estimated 3D feature location 1420 is simply theaverage of the closest points 1415 on each triangulation ray 1405, butany suitable triangulation method can be used.

For example, a calibration module 712 can triangulate an estimated 3Dposition by first solving a system comprised of equations of the form{right arrow over (p₀)}/t₀+{right arrow over (d₀)}≈{right arrow over(x)}/t₀ for each triangulation ray 1405 where {right arrow over (p_(n))}is the known vector ray origin position for the nth triangulationvector, {right arrow over (d_(n))} is the known unit vector of thedirection of the nth triangulation ray 1405, t_(n) is unknown the(scalar) approximate distance of the estimated 3D position along thetriangulation ray, and {right arrow over (x)} is the unknown estimated3D position for the triangulation. In some implementations, minimizingthe error of {right arrow over (x)}/t_(n) introduces a bias towardsfurther away estimated 3D positions (i.e. solutions with a greater depthare preferred to maintain consistency between the depth estimates foracross different images). In some implementations, to solve the systemof equations each t_(n) is assumed equal to each other t_(n), due to therelatively close proximity of cameras in image capture system 100,setting each t_(n), equal provides a good initial assumption. After thesystem of equations is solved to find an estimated {right arrow over(x)}, a nonlinear solver (or other suitable optimization method) can beused to iteratively optimize the estimated solution. In someimplementations, each t_(n), is now allowed to float (and is no longerassumed equal to each other t_(n)).

After a 3D location for each feature match of the possible match set iscalculated, for example by triangulating each feature match, thereprojection error of each feature match can be calculated. In thiscontext, the reprojection of a feature match refers to the expectedlocation within a calibration image that a feature at the 3D location ofthe feature match would be located. According to some embodiments,reprojection error is based on the difference between the expected andactual location (represented by the feature) of the feature. Thisreprojection error may be used as an estimate to show the likely errorsin the calibration, and as discussed below, when the reprojection errorfor a matching feature point significantly differs from other matchingpoints, it suggests the point may actually not be a strong match and maynot be considered for analyzing further calibration.

FIGS. 15A and 15B illustrate example reprojections and reprojectionerrors between feature points and reprojected points, according to oneembodiment. The calibration image 1500 of FIG. 15A comprises a featurepoint 1505, a reprojected point 1510, and a reprojection error 1515, aswell as a trace reprojected point 1520 and a trace reprojection errorwhich are discussed below.

In the example of FIG. 15A, the feature point 1505 is associated with afeature match which has been triangulated to a 3D location in space.Based on the current calibration of the image capture system 100 (inthis case, current knowledge about the position, orientation, and lenscharacteristics of the relevant camera 110), the estimated position ofthe 3D location within the calibration image 1500 can be determined.This estimated position is the reprojection point 1510. In someembodiments, a ray is generated from the triangulated 3D location to theimage sensor of the relevant camera 110 to determine the reprojectionpoint, but any suitable technique can be used. For example, areprojection point can be determined based on knowledge of the lenscharacteristics and field of view of the cameras 110, such as byassociating pixels of the calibration image with defined ranges ofangles from the centerline of the camera 110. In some embodiments, it isunlikely that the reprojection point 1510 and the original feature point1505 will be the same, therefore a reprojection error 1515 between thereprojection point 1510 and the feature point 1505 can be calculatedusing any suitable error calculation method. For example, the squarederror between the feature point 1505 and the reprojection point 1510 canbe used. This process can be repeated for to calculate the reprojectionerror for each other feature of the feature match. In some embodiments,the final reprojection error is the sum of the squared errors of eachfeature of the feature match. Reprojection error can also be calculatedwith respect to a trace reprojection point 1520 as described above.

Based on calculated reprojection errors, the possible match set can befurther refined. In some embodiments, feature matches with greater thana threshold reprojection error are discarded. The threshold reprojectionerror can be fixed or predetermined, or generated based on statistics ofthe possible match set such as thresholds set based on multiples of theaverage or median reprojection error. In some embodiments, a thresholdreprojection error can be determined separately for feature matchesbetween the same images. For example, the median reprojection error forthe set of feature matches between two given images is determined andfeature matches of the set with a reprojection error of greater thanfive times the median reprojection error between the two matches arediscarded. Based on this process, unreasonable (or outlier) featurematches are discarded from the set of feature matches resulting in a“reasonable match set” of pairwise feature matches.

The pairwise feature matches of the reasonable match set can now beassigned into “traces” or feature matches comprising 2 or more featurepoints. FIG. 16 is a graph illustrating an example trace, according toone embodiment. The graph 1600 is a plot of features of five camerascomprising the feature matches 1610-1650 and an assumed feature match1660. Each feature match 1610-1650 represents an example pairwisefeature match of a reasonable match set. For example, the feature match1610 represents a match between feature 3 of camera 1 and feature 1 ofcamera 3 and the feature match 1650 represents a match between feature 7of camera 4 and feature 4 of camera 5. Based a trace generationalgorithm, the calibration device 1110 can determine that the featurematches 1610-1650 are interconnected and form a trace. In someembodiments, the calibration device 1110 then generates assumed featurematches, even when those matches were not present in the initial featureset, based on the feature matches of the trace. For example, the assumedfeature match 1660 can be generated based on both feature 5 of camera 2and feature 7 of camera 4 being included in the same trace.

To determine a trace, the calibration device 1110 can use a tracegeneration algorithm to sequentially evaluate each pairwise featurematch to assign the associated features to a trace or use any othersuitable method to determine traces. For example, a trace generationalgorithm can determine if neither feature of the pairwise feature matchis assigned to a trace, both features are assigned to a new trace, ifone feature of the pairwise feature match is already assigned to atrace, the remaining feature is assigned to the same trace, and if bothfeatures of the pairwise feature match are already assigned to differenttraces, the traces are combined.

In some embodiments, the reasonable match set can be used to determine a“trace set” using the trace generation algorithm. Each trace of thetrace set can then be triangulated using the process described earlierto determine a 3D location for the trace. FIG. 14B illustrates anexample triangulation based on multiple triangulation rays, according toone embodiment. The environment 1450 of FIG. 14B comprises severaltriangulation rays 1455 originating from the 3D ray origins 1460 whichare estimated to pass in close proximity at the closest points 1465,resulting in the estimated 3D trace location at 1470. The process fortriangulating a trace can be similar to the described process fortriangulating two rays, with the addition of several more triangulationrays 1455. Now the 3D trace location 1470 can be reprojected into eachof the relevant cameras and new reprojection error for each featurematch of the reasonable match set can be calculated using the 3D tracelocation. In the example of FIG. 15A this is represented by the tracereprojection point 1520 and the trace reprojection error 1525.

Based on calculated trace reprojection errors, the reasonable match setcan be further refined as described above. For example, the median tracereprojection error between each pair of two images for the reasonablematch set can be determined and feature matches with a tracereprojection error of greater than five times the median tracereprojection error between their two images are discarded. Based on thisprocess, additional feature matches can be discarded from the set offeature matches resulting in a “refined reasonable match set” ofpairwise feature matches. In some implementations, if a feature match ofa trace is discarded, the entire trace (for example, including allfeature matches associated with the trace) is discarded.

According to some implementations, the trace generation algorithm isthen applied to the refined reasonable match set to generate a “refinedtrace set.” The refined trace set can comprise more or different tracesbased on the removal of pairwise matches from the reasonable match set.Therefore, removing matches can have the effect of “splitting” tracesi.e. separating a trace into separate traces in the refined trace set.The altered trace assignments of the refined trace set can alter orimprove the reprojection error of affected feature matches. For example,the revised trace reprojection error 1565 is much less than the tracereprojection error 1525, which can be the result of assignment of theassociated feature to a new or modified trace.

In some embodiments, the resulting “refined trace set” is used toiteratively optimize the calibration of the image capture system 100.For example, a standard nonlinear solver (or other suitable optimizationmethod) can be used to minimize the reprojection error for matches ofthe refined trace set by adjusting various parameters of thecalibration. The revised calibration is then used to initialize a newiteration of the optimization, starting from the initial feature set,according to some embodiments. In some embodiments, the calibrationparameters to be optimized include camera orientation, camera position,and various lens corrections such as lens distortion, lens centering,and lens image scale. In some embodiments, each iteration additionallyincludes the triangulated positions of each trace or match of therefined trace set to aid the nonlinear solver in converging to asatisfactory solution for the iteration. The parameters the nonlinearsolver optimizes over can vary based on the iteration of the calibrationprocess, for example, in the first iteration of the calibration processthe nonlinear solver of the first iteration can optimize over fewerparameters (such as the parameters assumed to have the largest variance)than the later iterations, which can introduce more granular parameters.For example, the first iteration of the calibration process can optimizecamera orientation only, the second can optimize camera orientation andposition, and the third (and further iterations) can optimize cameraorientation, camera position, and lens corrections. Similarly,iterations can optimize parameters in a fixed pattern, or in any othersuitable order. In some implementations, certain parameters can bechanged on a per-camera basis (such as camera position and orientation),while others (such as lens distortion) can be globally used for allcameras at once or for a set of cameras at once (such as all cameras ofthe image capture system 100 using the same lens design).

In some implementations, a predetermined number of iterations of thecalibration process occur, for example 10 iterations. In each iterationof the calibration process, the set of initial feature matches isrefined based on the updated calibration of the image capture system 100and a new or different refined trace set can result, according to someembodiments. In other embodiments, iterations of the calibration processoccur until the final change in calibration parameters is less than athreshold amount, or until any other suitable condition is met.

FIG. 17 is a flowchart illustrating an example process for calibratingan image capture system, according to one embodiment. The process ofFIG. 17 begins when a calibration set of calibration images are captured1710 at the image capture system and received by the calibration device1110. Then, an initial feature set is generated by identifying 1720 andmatching 1730 feature points between the calibration images of thecalibration set. The camera calibration parameters are initialized 1730to provide an initial calibration of the image capture system. Then thecalibration is iteratively revised 1750 based on the initial calibrationand initial feature set. Finally the optimized calibration is applied1760 to the image capture system and stored.

FIG. 18 is a flowchart illustrating an example calibration process foriteratively improving the calibration of an image capture system,according to one embodiment. The process of FIG. 18 begins when theinitial camera calibration and the initial feature set of pairwisematches are received 1810, 1820. Then the initial feature set can berefined 1830 based on expected overlap between the calibration images togenerate the possible match set. Next, 3D positions for each match ofthe possible match set can be triangulated 1840, and the possible matchset can be refined based on the projection error of each match, formingthe reasonable match set. Traces are then identified between multiplefeatures (comprising multiple matches) are then identified 1850 formingthe trace set. 3D positions for the traces of the trace set can then beidentified by triangulation 1860, and the set of traces is refined basedon the reprojection error for each trace. Finally, the cameracalibration can be iteratively improved 1870 based on the refined traceset. Further iterations of the calibration process 1880 can be startedfrom the step 1820, beginning with the original feature match set butthe newly updated calibration parameters.

Depth Calculation

To calculate depth maps for captured images from the image capturesystem 700, the depth calculation module 716 of the image processingsystem 710 can employ a technique to progressively refine a depthestimate by beginning with a small-resolution image and scaling thedepth estimates to larger-resolution images. The large-to-smallresolution images may be represented as an “image pyramid” that isprogressed up in determining the depth estimates.

FIG. 19 illustrates an example image pyramid, according to oneembodiment. The image pyramid 1900 of FIG. 19 comprises three successivelevels 1910, 1920, and 1930. Each level of the image pyramid 1900 cancomprise the same images in progressively lower resolutions, i.e. thefirst level 1910 comprises a set of images and the second level 1920includes lower resolution versions of the same set of images. In theimage pyramid 1900, the first level 1910 comprises the images 1912-1916,the second level 1920 comprises lower resolution versions 1922-1926, andthe third level 1930 comprises the lowest resolution images 1932-1936.The image pyramid 1900 has three levels for example purposes, but animage pyramid can have any suitable number of levels, for example 10 or15 levels.

The first level 1910 of an image pyramid 1900 comprises the highestresolution images in the image pyramid. For example, the first level1910 can comprise the input images captured by the image capture system100 at full resolution. In other embodiments, the first level 1910 cancomprise the input images downsampled to a reduced size (e.g., by ascaling factor) of the original images captured by the image capturesystem 100. For example, the first level 1910 can comprise images 25% ofthe scale of the original captured images (a scale factor of 0.25), butany suitable starting scale factor can be used. Starting the imagepyramid at a 0.25 scale factor will result in a depth map at 25% of thescale of the original input images (i.e. depth for the input image iscalculated in 4×4 pixel blocks).

To generate a lower level of the image pyramid 1900 the images of theprevious level can be downsampled 1940 to generate a lower resolutionversions for inclusion in the lower level of the image pyramid 1900. Forexample, the second image 1914 can be downsampled 1940 to become the lowres. second image 1924, which can be further downsampled to be thelowest res. second image 1934. According to some implementations, eachsuccessively lower level of an image pyramid 1900 can be at a specificscale factor of the previous (higher resolution) level, for example a0.75 or 0.90 scale factor, where each lower level is 75% or 90% the sizeof the previous level. Calculation of an image pyramid can continueuntil a threshold number of levels is reached (for example, 20 levels),or until a lower resolution level would fall below a thresholdresolution in one dimension (for example 100 pixels). Based on the imagepyramid 1900, depth maps can be calculated for each image, starting atthe lowest resolution level of each image, and progressively beingrefined towards the higher resolution levels of the image pyramid 1900.

To calculate or refine a depth map for a given image (hereinafter, thereference image), images with overlapping field of views to thereference image (hereinafter, overlap images) can be reprojected to theviewpoint of the reference image. For example, the process ofreprojection can project the overlap image into space based on theposition and orientation of the camera that captured the overlap image.Then the projected overlap image can be reprojected to the viewpoint ofthe reference camera. The reprojected overlap images can then be used tocalculate or refine the depth map for the reference image.

FIG. 20 illustrates an example reprojection of overlap images to areference image, according to one embodiment. The environment of FIG. 20includes a reference image 2010, overlap images 2020 and 2030,reprojected overlap images 2025 and 2035, and reprojected overlap images2040 and 2045.

According to some embodiments, overlap images such as the overlap images2020 and 2030 are identified based on the relative position,orientation, and field of view of the reference camera (i.e. the camera110 which captured the reference image 2010) and the overlap cameras(i.e. the cameras 110 which captured the overlap images 2020 and 2030).To reproject the overlap images 2020 and 2030, the overlap images can beprojected into 3D space based on an existing depth map for the overlapimages 2020 and 2030 or, in other embodiments, based on an assumption ofthe depth for the overlap images 2020 and 2030. For example, in someembodiments, each overlap image 2020 and 2030 is treated having aninfinite distance from the overlap camera. Then, the overlap image isreprojected 2040 or 2045 based on the position of the reference camerarelative to the overlapping camera to generate the reprojected overlapimages 2025 and 2035. For example, the overlap image 2020 and thereference image 2010 overlap in the estimated overlapping area 2022.When reprojected, the overlap image 2020 is reprojected 2040 to theviewpoint, resulting in the reprojected overlap image 2025 comprising anapproximation the overlapping portion of the reference image 2010 usingthe estimated overlapping area 2022 of the overlap image 2020. Thereprojected overlap images 2025 and 2035 can be used both to generate aninitial depth map for the reference image 2010 and to refine the depthmap of the reference image 2010.

To begin the depth map refinement process, an initial depth map isgenerated for each image of the lowest resolution level of the imagepyramid 1900, according to some embodiments. In some implementations,depth map initialization can utilize “brute force” techniques that wouldnot be practical at higher resolution levels of the image pyramid 1900,for example due to increased requirements for storage or computationpower when initializing a depth map for a higher resolution image.

In some embodiments, depth map initialization for a given referenceimage can begin by identifying and reprojecting all overlap images tothe viewpoint of the reference image. To evaluate a potential depth fora pixel in the reference image 2210, the possible depth value is appliedto the reference image to determine the corresponding pixel in thereprojected overlapping image. As discussed below, the pixel of thereference image is compared to the corresponding pixel in thereprojected overlapping image based on a cost function that mayincorporate a variety of factors that assess the likely accuracy of thecorrespondence of the reference image pixel to the overlapping image.

To initiate the depth map at the lowest resolution of the image pyramid,the cost may be evaluated for each possible corresponding pixel in anoverlapping image. For example, the cost may be determined based oncandidate depths that designate each possible pixel in the overlappingimage as a corresponding pixel. As an alternative, the possible depthmay be incremented, for example by constant increments of 1/d, toidentify candidate corresponding pixels in the overlapping image. Sincethe lowest level of the image pyramid may have a relatively smallresolution, such as 100×100, this may be performed without extensivecomputational time. Using the calculated costs, a depth estimate may beset for the pixel in the reference image that had the lowest calculatedcost.

In some embodiments, the depth calculation module 716 begins calculatingdepth maps for a set of images by generating an image pyramid 1900.Then, initial depth maps are generated for each image of the lowestresolution version of the image pyramid 1900. Based on the initial depthmaps, the depth calculation module 716 then begins to refine the initialdepth estimates for each image of the image pyramid 1900. In someembodiments, the depth calculation module 716 upscales the initial depthestimates to the resolution of the next layer of the image pyramid 1900to further refine each depth map. In some implementations, each depthmap is then checked for consistency with the other depth maps of thesame level of the image pyramid. For example, the depth maps of eachoverlapping view can be reprojected to the reference camera viewpointand the reprojected depth estimates can be compared to the current depthestimates (for example, using a cost functions as discussed below), thenthe lowest cost depth estimate can be adopted.

To refine a calculated depth map for a given reference image, the depthcalculation module 716 can proceed sequentially through the pixels ofthe reference image in a defined order, refining the depth estimate foreach pixel. FIG. 21A illustrates an example order to refine the depthestimation of pixels of an image, according to one embodiment. The depthmap 2100 of FIG. 21A comprises a plurality of pixels including theexample pixel 2110, the first refined pixel 2120, and the last refinedpixel 2125 which are evaluated sequentially based on the traversal order2130. According to some implementations, the depth map 2100 isassociated with a corresponding reference image in an image pyramid1900, where each pixel of the depth map 2100 holds a depth estimate (forexample in 1/d format) for the corresponding pixel of the referenceimage. In the example of FIG. 21A, the pixels of the depth map 2100 arerefined based on the traversal order 2130, starting in the upper leftwith the first refined pixel 2120 and proceeding right and down, endingat the last refined pixel 2125. According to some embodiments, aftereach pixel of the depth map 2100 is evaluated according to the traversalorder 2130, the depth map 2100 can be further refined in reversetraversal order, i.e. progressing left and up from the last refinedpixel 2125 to the first refined pixel 2120. Refining the depth map 2100both in traversal order 2130 and reverse traversal order can allowimprovements in the depth map 2100 to propagate through the entire depthmap 2100.

To refine the depth estimate for a given pixel of a depth map 2100, forexample the example pixel 2110, the depth calculation module 216 canfirst consider proposals from neighbors of the example pixel 2110. FIG.21B illustrates an example pixel with proposals from neighboring pixels,according to one embodiment. FIG. 21B comprises an example pixel 2110and the left and upper neighbors 2150 and 2155 of the example pixel2110. In some implementation, proposals are taken from neighbors of theexample pixel 2110 which have already evaluated in the traversal order2130, in this case the left neighbor 2150 and the upper neighbor 2155 asthose pixels have already been evaluated in prior to the example pixel2110. Similarly, when evaluating in reverse traversal order, proposalsfrom the lower and right neighbors can be considered. In someembodiments, other suitable proposals are also considered, such asrandom permutations of the current depth estimate for the example pixel2110, or any other suitable proposal.

After the depth proposals are identified for the example pixel 2110 (forexample, the set of depth proposals can include the current depthestimate as well as depth estimates from appropriate neighbors of theexample pixel 2110) each depth proposal can be evaluated based on a costfunction to determine the best proposal, i.e. the proposal with thelowest cost as measured by the cost function. The lowest cost proposalis then adopted as the depth estimate for the example pixel 2110 and thedepth estimate is further refined by performing one step of a gradientdescent process for the current pixel based on the gradient of the costfunction. Any suitable method of gradient descent can be used, howeverin some implementations, only one gradient descent step (or any othersuitable limited number of gradient descent steps) is performed.Limiting the rate of convergence of the depth map by performing only onestep of gradient descent for each pixel of the depth map 2100 each timeit is evaluated can reduce unnecessary computations, as the depthestimate will converge across levels of the image pyramid, and based onrefinements in the depth map of the neighboring pixels, which can betaken as proposals to the current depth estimate.

After each pixel of the depth map 2100 is refined, for example accordingto both the traversal order 2130 and the reverse traversal order, thedepth map 2100 can be filtered using a median filter, a joint bilateralfilter, or any other suitable type of filter to blur the depthestimates. The filter may be edge-or time-aware and such filtering isdiscussed in further detail below. After the depth map 2100 has beenrefined and filtered, the depth calculation module 716 progresses to thenext (higher resolution) level of the image pyramid 1900 and upscalesthe depth map 2100 to serve as an initial depth map for thecorresponding reference image of the next level of the image pyramid1900.

A cost function, according to some embodiments, can be any suitablefunction which takes an input of the current depth estimate for a pixelof a depth map 2100 and returns a “cost” or measure of quality of theinput depth estimate. A cost function can have many terms based on thecurrent depth estimate, and each term can require one or more additionalinputs other than the current depth estimate such as depth estimates forneighboring pixels of the depth map 2100, values from the currentreference image or information derived from one or more images or otherdatasets specifically calculated to aid in cost function calculation(hereinafter, “features”). Features can include reprojected overlapimages, filtered or processed versions of the reference image, filteredor processed versions of the reprojected overlap images, or any othersuitable feature, such as the results of a deep learning model appliedto the current depth map. Features for calculating the cost function caninclude, for example, the intensity of the reference image (i.e. agrayscale or a one channel version of the reference image), theintensity gradient (or the magnitude of the intensity gradient) of thereference image, a blurred reference image, and the intensity, intensitygradient, or magnitude of the intensity gradient of the reprojectedoverlap images. Appropriate features for depth map evaluation can becalculated as the image pyramid 1900 is generated, as needed, oraccording to some implementations, as the depth map for each image ofthe current level of the image pyramid 1900 is initialized. In someimplementations, suitable features for cost function evaluation arecalculated based on the image set for the current level of the imagepyramid 1900; i.e. the resolution of calculated features can match thecurrent resolution of the reference image and associated depth map 2100.

In some embodiments, the cost function includes one or more depthaccuracy terms to measure the accuracy of the current depth estimatebased on difference between the current pixel of the reference image andthe corresponding pixel in one or more reprojected overlap images.Therefore, the depth calculation module 716 can determine the pixel ineach reprojected overlap image which corresponds to the current pixelbased on the current depth estimate. FIG. 22A illustrates an examplereference image with a reprojected overlap image overlaid, according toone embodiment. The reference image 2210 of FIG. 22A includes areprojected overlap image 2220 overlaid over the reference image 2210.In some implementations, the overlap image is reprojected with aninfinity depth assumption (i.e. during the reprojection process thedepth of each pixel of the overlap image is assumed to be infinity), andtherefore the reprojected overlap image 2220 does not perfectly alignwith the reference image 2210, producing a difference 2230 between thereference and reprojected images. For any objects far in the distance inthe reference image 2210 (i.e. features closer to infinity depth) theinfinity depth assumption reprojection is relatively accurate, howeverfor other, closer objects, for example, the person or the tree in thereference image 2210, there is a marked difference 2230.

Based on a depth map for the reference image 2210, the depth calculationmodule 716 can correct for the differences 2230 between the referenceimage 2210 and the reprojected overlap image using a suitablemathematical process. The depth calculation module 716 can find thecorresponding pixel to each pixel of the reference image (the differencebetween a pixel in the reference image 2210 and the estimatedcorresponding pixel in a reprojected overlap image is hereafter referredto as a “depth correction”). The magnitude of a calculated depthcorrection can be based on the relative positions of the reference andoverlap cameras, the current depth estimate, and any other suitablefactor. For example, FIG. 22B illustrates an example reference imagewith an applied depth map, according to one embodiment. The referenceimage with applied depth map 2250 of FIG. 22B comprises a correctedimage 2260 which can be the reprojected overlap image corrected based onthe depth map of the reference image 2210. In this example, thecorresponding pixels in the reprojected overlap image are shifted by theappropriate depth correction to the location of their counterparts inthe reference image. Based on the correction, the difference between theoverlap and reference images is much smaller. The remaining differencebetween the reference and overlap images can be viewed as a measure ofthe accuracy 2270 of the depth map for the reference image 2210.

Similarly, the depth calculation module 716 can determine acorresponding pixel in a reprojected overlap image based on the currentdepth estimate. Features of the current pixel in the reference imagereference image and the corresponding pixel in a reprojected overlapimage can be compared to evaluate the accuracy of the depth estimate ofthe current pixel.

One or more depth accuracy terms of the cost function compare variousfeatures (such as intensity, intensity gradient, color values, or thelike) of the current pixel in the reference image to the correspondingpixel in a reprojected overlap image, according to some embodiments. Insome embodiments, the cost function comprises multiple weighted depthaccuracy terms, for example one depth accuracy term for each reprojectedoverlap image.

For example, a depth accuracy term associated with a first reprojectedoverlap image can comprise RGB comparison terms of the formc_(R)∥R_(R)−R₀₁∥²+c_(G)∥G_(R)−G₀₁∥²+c_(B)∥B_(R)−B₀₁∥², where G_(R) isthe value of the green channel in the reference image (at the currentpixel), G₀₁ is the value of the green channel in the corresponding pixelof the first reprojected overlap image, and c_(G) is a predeterminedweighting coefficient for the green channel (in this example similarconventions are followed for the red and blue channels).

Similar terms can be included in the depth accuracy term for any otherdesired channel or feature of the reference image, for example,c∥u_(R)−u₀₁∥² and c∥v_(R)−v₀₁∥² can be used to include optical flowinformation, in this example stored in additional channels u and v ofeach image. Additionally, the depth accuracy term can include anintensity comparison term of the form c_(I)∥I_(R)−I₀₁∥² where Irepresents the intensity feature, which is a one channel representationof an RGB image, generated, for example, by a weighted combination ofeach color (RGB) channel of the image. In some embodiments, the depthaccuracy term includes an intensity gradient term, c_(∇1)∥∇I_(R)−∇I₀₁∥²where ∇I represents the gradient of the intensity or the magnitude ofthe gradient of the intensity.

A cost function can also include additional suitable terms, for examplesmoothness terms, regularization terms, and other terms. A smoothnessterm can be of the form c_(S)∥d−d_(B)∥² where d represents the currentdepth estimate and d_(B) represents a blurred depth estimate (forexample, from a blurred version of the current depth map). Similarly, aregularization term can be of the form c_(reg) (1/d) where d representsthe current depth estimate and the regularization term is weighted toprefer further depth estimates. In some implementations, a varianceweighted regularization term is used of the form c_(reg)(1/d)/(1+c_(v)var) where var is the variance of the depth map at thecurrent pixel (computed using any suitable method). Using varianceweighted regularization can improve the temporal stability of the finaldepth map over time (i.e. depth maps over time are more consistent witheach other). Additionally, a cost function can include any othersuitable term, such as a term using a feature map generated from a deeplearning model.

In some implementations, the gradient of the cost function is alsodetermined, for example to perform gradient descent steps to refine thedepth map. The gradient of the cost function can be determined from thecost function using any suitable method.

FIG. 23 is a flowchart illustrating an example process for determining adepth estimate for a set of images based on an image pyramid. Theprocess of FIG. 23 begins when an image set is received 2305 and theimage processing system generates an image pyramid for the image set.For example, the image set can be a set of simultaneously capturedimages (for example, corresponding frames of simultaneously capturedvideo) for depth calculation. Then, for the smallest (lowest resolution)level of the image pyramid, a depth map for each of image of the imageset is initialized 2310 by the image processing system using a bruteforce method. The next (higher resolution) level of the image pyramid isselected 2320 for refinement, and a reference image from the currentlevel of the image pyramid is selected 2330. Additionally, any overlapimages for the selected reference image are identified by the imageprocessing system. Then the image processing system then can reproject2340 the identified set of overlap images and generate any otherfeatures needed to refine the depth estimates. The previous level depthestimate for the reference image can then be upscaled 2350 to theresolution of the current level of the image pyramid and in someembodiments, checked against depth maps for the other images of thecurrent level. Then, a matching algorithm is used 2360 to refine thedepth map for the reference image. Finally, the depth map is filtered2370, for example, using a median filter and a joint bilateral filter.If there are more images 2380 in the image set, a new reference image isselected. Otherwise, the next (higher resolution) level 2390 of theimage pyramid is selected.

FIG. 24 is a flowchart illustrating an example process for refining thedepth estimate of an image, according to one embodiment. The process ofFIG. 24, begins when the depth calculation module of the imageprocessing system receives 2410 a reference image, a depth map for thereference image, and calculated features for the reference image. Then aspecific sequential order of pixels in the reference image is selected2420. The depth calculation module can select 2430 the next pixel in thedetermined order and evaluate 2440, using a cost function, a set ofproposals, including the current pixel depth estimate a neighboringpixel depth estimates. Based on the cost of each proposal, the depthcalculation module selects 2450 and adopts the best proposal as thedepth estimate for the current pixel. The depth estimate is then refined2460 by performing one gradient descent step using the gradient of thecost function and adopting the result as the new depth estimate for thecurrent pixel. If all pixels are refined 2470, the process is repeated2480 in reverse pixel order and the refined depth map is returned 2490.

FIG. 25 is a flowchart illustrating an example process for maintainingconsistency between depth estimates, according to one embodiment. Theprocess of FIG. 25 begins when the depth calculation module retrieves2510 a reference image and upscaled depth maps for the images of thecurrent image pyramid level including, for example, depths map for thereference image and one or more overlap images of the reference image.Then, the depth maps of the overlapping images are reprojected 2520 tothe reference camera viewpoint. Then a pixel in the current depth map isselected 2350 and the corresponding depth estimates in the reprojectedoverlap depth maps are determined. The depth calculation module can thenevaluate 2540 the current depth estimate and the reprojected depthestimate using a cost function. Based on the results of the evaluation,the best depth estimate (from the current depth estimate and thereprojected depth estimates) is adopted 2550. If all pixels areevaluated 2560, the process ends, otherwise a new pixel is selected forevaluation.

FIG. 26 illustrates an example process for filtering a depth map basedon a guide, according to one embodiment. The process of FIG. 26 is anexample of a joint bilateral filter process a depth map 2610 based on aguide image 2620, although in other embodiments, any suitable jointbilateral filter can be used. To filter the depth map 2610, each pixelof the depth map is filtered using a kernel generated for that pixel ofthe depth map based on the corresponding pixel of the guide image 2620and its surrounding region. For example, the selected pixel 2615 can befiltered based on a kernel 2635 generated based on the correspondingpixel 2625 in the guide image 2620. Based on a kernel generationfunction 2630 and the corresponding pixel of the guide image (and thesimilarities of the surrounding region of the guide image 2620 to thecorresponding pixel 2625), the kernel 2635 is generated. When the kernel2635 is applied to the selected pixel 2615 and the surrounding region inthe depth map 2610, the filtered pixel 2645 of the filtered depth map isdetermined. In some embodiments, the kernel 2635 is 3D, i.e. in the caseof a time dependent filter.

For example, the guide image can be any suitable feature, for example adepth map 2610 can be filtered using the reference image associated withthe depth map 2610, with an optical flow map of the reference image (ordepth map), with a feature map generated based on applying a deeplearning model to the reference image (or depth map), or any othersuitable guide image 2620 or combination of guide images 2620.

FIG. 27A illustrates an example process for training a set of transformsto filter a depth estimate, according to one embodiment. In the examplesof FIGS. 27A and 27B, a set of image transforms is used to generate afeature map of an image to learn an improved guide for a joint bilateralfilter of a depth estimate. The process of FIG. 27A can begin when atraining image 2710 associated with a previously known training depthestimate 2715 is received. The training image 2710 is input into a setof image transforms 2720 to generate a feature map 2725 for the trainingimage. The image transforms 2720 may include various modifications andanalyses of an image to generate a map of features for the jointbilateral filter. The image transforms are trained to learn the relevanttransforms and weights thereof to generate a feature map 2725 useful toimprove a depth estimate. The set of transforms may include varioustensor or matrix transforms for the image structures that aresequentially performed to generate the depth guide. These transforms mayinclude convolutional layers, pooling layers, subsampling, feed-forward,and other image processing or ‘deep learning’ transforms of the image.The image transforms may include weights and other learned parametersfor performing the transforms from the training image 2710 to thefeature map 2725.

In some embodiments the feature map 2725 has the same dimensions as thetraining image, and can comprise multiple features associated with eachpixel of the input image (in this case the training image 2710).According to some implementations, the training depth estimate 2715 isauthoritative for training purposes and assumed to be true. For example,the training depth estimate can be from labeled data (i.e., fromwell-labeled training sets of data having depth information for images),or generated from a 3D computer rendering, where the depth forindividual pixels can be precisely calculated in the digital 3Denvironment. The training depth estimate 2715 can be perturbed by randomnoise 2730 to produce an imperfect noisy depth estimate 2735 to befiltered by the deep-guided joint bilateral filter (JBF) 2740. The noisydepth estimate 2735 is filtered by the deep-guided JBF 2740 using thefeature map 2725 as a guide 2725 to generate the predicted depthestimate 2745.

By comparing the training depth estimate 2715 to the predicted depthestimate 2745 (created by the noisy depth estimate 2735 guided by thetransformed training image), the image transforms can be trained toimprove the similarity of the predicted depth estimates to training(i.e., known) training depth estimates. The training may modify theweights and other parameters of the image transforms 2720. Whenperformed across a range of training images and comparing the depthestimates across the pixels of the training images, the image transforms2720 learn the weights that improve the filtering of the noisy depthestimate 2735.

FIG. 27B illustrates an example process for using a set of transforms tofilter a depth estimate, according to one embodiment. The process ofFIG. 27B begins when a reference image 2750 is input into a set oflearned image transforms 2760 to generate a feature map 2765 for thereference image 2750. The learned image transforms 2760 are the imagetransforms 2720 after the training process of FIG. 27A determines theappropriate weights and parameters for the image transforms. Thegenerated feature map 2765 can be used as a guide to filter the currentdepth estimate 2755 using a deep-guided JBF 2770 to generate theimproved depth estimate 2780. In addition to use as a filter, theimproved depth estimate 2780 may also be used as a component of a costfunction for evaluating a depth estimate as discussed above with respectto the depth map generation. That is, the cost function may increasewhen a proposed depth varies from the value of the improved depthestimate 2780, incentivizing the cost function to confirm with theimproved depth estimate 2780 pixel value but permitting other factors inthe cost function to outweigh the improved depth estimate when otherfactors suggest a strong improvement to the depth estimate.

Rendering

The rendering module 718, according to some embodiments, processes areceived image set of a scene, for example, an image set captured by theimage capture system 100, to generate one or more render viewsrepresenting the scene. In some implementations, each image set forrendering has an associated set of generated depth maps including adepth map for each image of the image set. For example, an image set canbe associated with a set of depth maps generated by the depthcalculation module 716 (or from another suitable source). A render viewof a scene can be any image depicting the scene to a viewer of therender view. For example, a render view can allow the scene to berecreated in a head-mounted display (HIVID), for example, through apanoramic, spherical panoramic, or suitably wide angle image (such as animage to be displayed as an eye view by a HIVID). In someimplementations, a render view is an image output in cubemap,equirectangular, or cylindrical formats in resolutions such as “8K” (forexample 8192 by 8192 pixels), or any other suitable resolution. Therender view thus can represent the scene as captured by the imagecapture system 100. The rendering module 718 may generate two (or more)render views based on a given image set from one or more definedviewpoints; for example, a render view can be generated from viewpointsfor each of a user's eyes, thus providing a pair of stereoscopic imagesfor viewing using a HIVID device. For some output projections, asections of a single render view may be rendered from multipleviewpoints, for example to approximate a user's eye view of a scene in a360 degree panoramic image. In some implementations, render viewpointscan be associated with any suitable 3D position, for example, a renderviewpoint can be selected based on a tracked position of a user's head,based on a desired viewpoint of a scene other than a camera viewpoint,or any other suitable location. In other embodiments, a render view canbe any image generated from multiple images of the image set by therendering module 718. According to some embodiments, depth maps (orother depth information) for the images of an image set can allowvarious depth-based effects to be applied to a render view. For example,a render view can be split into multiple images based on depthinformation, for example, a separately generated foreground image andbackground image each with a defined range of depicted depths (such as0-30 feet for the foreground image and 30 feet—infinity for thebackground image). Similarly, a render view may have the backgroundremoved (and or replaced with other suitable image information) based ondepth information (possibly in combination with other techniques), forexample rendering areas of the render view with an associated depthgreater than a threshold depth as white or transparent. Similarly,render views can have depth-based fog or other virtual objects insertedinto the scene based on the depth information.

To generate a render view, any suitable rendering method can be used bythe rendering module 718, including ray tracing methods (for example,using a ray marching algorithm to compute intersections between rays anddepth maps), forward splatting methods, triangle rasterization methods,or any other suitable rendering methods. Similarly, the rendering module718 may utilize hardware acceleration methods to speed up the process ofrendering an image set. In some embodiments, rendering may occur inrealtime or substantially in realtime based on render views requestedfrom a client device. For example, the rendering module 718 can receiverender viewpoints from a client HMD device representing stereoscopicviews for presentation using the client HMD device. In response, theclient HIVID device can render a scene from a predetermined image setwith previously calculated depth maps, for example, the next frame in asynchronized video captured by the image capture system 100.

FIG. 28 illustrates an example environment in which a scene is renderedfrom a set of depth surfaces. The environment 2800 of FIG. 28 comprisesa plurality of cameras 2810 each associated with a projected depthsurface 2815. A render view can be rendered from the render viewpoint2820 based on the projected depth surfaces 2815.

In some implementations, a depth surface is generated for each image ofthe image set to be rendered. Herein, a depth surface is a 3D surfacegenerated based on a reference image (such as an image captured by theimage capture system 100), a depth map associated with the referenceimage (for example, a depth map generated based on the reference imageby the depth calculated module 716). In some embodiments, a depthsurface is additionally generated and oriented in 3D space based oncamera calibration information about the camera that captured thereference image (for example, the position, orientation, and lensinformation of the camera). A depth surface can be rendered as aconnected mesh of triangles, where each triangle of the depth map sharescolor information with an associated pixel of the reference image. Insome implementations, two connected triangles are associated with eachpixel of the reference image and the triangles are oriented in 3D spaceto approximate the associated pixel when viewed from the viewpoint ofthe capturing camera. A depth surface, according to some embodiments,can approximate the reference image projected into space based on theassociated depth map. For example, in the embodiment of FIG. 28, each ofthe projected depth surfaces 2815 approximate their associated camera2810. Viewing one of the projected depth surfaces 2815 from theperspective of the associated camera 2810 would provide an approximationof the reference image.

FIG. 29 is an illustration of a render view comprising a rendered depthsurface, according to one embodiment. The render view 2910 of FIG. 29comprises a rendered depth surface 2920 with an occluded area 2925. Inthe embodiment of FIG.29, the rendered depth surface 2920 is made up ofa set of triangles 2930. The rendered depth surface 2920 is shown asextending outside of the render view 2910 in FIG. 29, however in someimplementations areas of a depth surface outside the render view wouldnot be calculated when rendering the depth surface.

The rendered depth surface 2920, according to this example, alsocomprises an occluded area 2925 of the depth surface which is notvisible in the render view 2910. The occluded area 2925 may be generatedbecause the view from the camera viewpoint differs from the view fromthe render viewpoint. For example, from a capturing camera's viewpoint,the rendered surface may have varying depths, but because the varyingdepths generate a three-dimensional rendered depth surface 2920, fromthe render viewpoint portions of the depth surface may appear behind acloser portion of the depth surface from the perspective of the renderviewpoint. Different rendering methods may handle an occluded area 2925differently. For example, the rays of a ray tracing method may strikethe “upper,” non-occluded area of the depth surface first, therefore theoccluded area 2925 is never rendered in the rendered depth surface. Incontrast, “forward splatting” or “triangle rasterization” renderingmethods may implement a “z-buffering” technique where the triangles ofthe rendered depth surface 2920 are rendered from furthest to closest,resulting in the occluded area 2925 being rendered, then covered up bylater rendered triangles.

FIG. 30 is an illustration of a render view comprising a set of blendedrendered depth surfaces, according to one embodiment. As shown in FIG.30, multiple rendered depth surfaces may correspond to the renderviewpoint. The render view 3010 of FIG. 30 comprises a first rendereddepth surface 3020 and a second rendered depth surface 3030 whichoverlap at an overlapping area 3040. Each rendered depth surface 3020and 3030 also includes an alpha channel blending area 3045.

To generate the final render view 3010 the set of rendered depthsurfaces (here, including the first and second rendered depth surfaces3020 and 3030) are overlaid and combined to generate the render view3010. In some implementations, the rendered depth surfaces are combinedtogether based on an alpha channel associated with each pixel of therendered depth surfaces. For example, a rendered depth surface can havean alpha channel blend 3045 around the edge of the rendered depthsurface. An alpha channel blend can gradually reduce the alpha channelof pixels of a rendered depth surface to 0 based on the distance fromthe given pixel to the edge of the rendered depth surface. In otherembodiments, the alpha channel for a pixel of a rendered depth surfacecan be scaled from 1 to 0 as a function of the distance from the centerof the rendered depth surface, resulting in a circle or oval shapedalpha “cone” for the rendered depth surface. In some implementations,the alpha channel blend 3045 aids in smoothly combining overlappingdepth surfaces. Similarly, rendered depth surfaces determined to befarther away in depth from the render viewpoint of the render view 3010can be assigned a lower overall alpha value than other rendered depthsurfaces determined to be closer to the render viewpoint, according tosome embodiments. Combining the rendered depth surfaces can, forexample, be accomplished using a weighted average by alpha value, or byany other suitable method. For example, rendered depth surfaces can becombined using an equation of the form v=α₁v_(S1)+α₂v_(S2) . . . /α₁+α₂. . . where v is the final value for a pixel of the of the render view3010 (in some implementations, v may be a vector including multiplechannels of color information), v_(Sn) is the value for that pixel fromthe nth rendered depth surface (for example, v_(S1) represents the valuefrom the first rendered depth surface 3020), and α_(n) is the alphachannel value for that pixel in the nth rendered depth surface. In someimplementations, pixels of the nth depth surface that do not intersectwith the nth depth surface are assigned values α_(n)=0 and v_(Sn)=0. Inother implementations, exponential or softmax combination functions canbe used to combine rendered depth surfaces based on an alpha channel.

Similarly, an accumulation method can be used to reduce needed memoryand storage space for rendering. Some implementations use a set of twoaccumulation images, the first accumulation image storing a runningtotal of acc₁=α₁v_(S1)+α₂v_(S2) . . . for each pixel of the render viewas each successive rendered depth surface is calculated. Similarly, thesecond accumulation image can store a running total of acc₂=α₁+α₂ . . .for each pixel of the render view as each successive rendered depthsurface is calculated, according to some embodiments. For example, afterthe first depth surface is calculated acc₁ can store the value α₁v_(S1)for each pixel and acc₂ can store the value α₁ for each pixel. After thesecond depth surface is rendered, acc₁ can store the valueα₁v_(S1)+α₂v_(S1) for each pixel and acc₂ can store the value α₁+α₂ foreach pixel, and so on. When all depth surfaces have been calculated,acc₁ can be divided by acc₂ to determine the final values of the renderview 3010.

In some situations, for example, where a depth surface is rendered froma viewpoint different in angle from the camera viewpoint, continuouslyrendered depth surfaces (that is, a depth map rendered as a singlesurface without separations or breaks) can give a “false depth”resulting from discontinuities or sharp changes in depth between pixelsin the depth surface. FIG. 31A illustrates an example depth surface withdiscontinuities around an obstructing object, according to oneembodiment. The environment of FIG. 31A comprises a camera 3105capturing an image of an obstructing object 3120 in front of abackground object 3125. A depth map is generated based on the imagecaptured by the camera 3105, which is used to render a depth surface3150. In this example, the generated depth map is fairly accurate, asthe obstructing object 3120 blocks the camera 3105 view of portions ofthe background object 3125. However, the resulting depth surface 3150includes several discontinuities or sharp changes in depth estimatewhere the reference image transitions between the obstructing object3120 and the background object. In the embodiment of FIG. 31A, the depthmap 3150 is continuously rendered and therefore the depth surface 3150is rendered including the discontinuities.

When the depth surface 3150 is rendered from a render viewpoint 3110 ata different angle 3115 than the camera 3105 viewpoint discrepancies canoccur between the rendering of the depth surface 3150 and the actualscene comprising the obstructing and background objects 3120 and 3125.For example at the depth surface intersection 3140, the correctrendering point 3130 occurs with a substantial rendering error 3135 whencompared to the actual scene. In some implementations, even ifadditional depth surfaces with the correct rendering point 3130 exist,the rendered depth surface 3150 would distort the rendering of that areaof the final rendered image.

Therefore, a discontinuity correction method can be applied whengenerating a depth surface from a depth map. FIG. 31B illustrates anexample depth surface with discontinuity correction, according to oneembodiment. The environment of FIG. 31B includes the same camera 3105and scene comprising the obstructing object 3120 and background object3125 as FIG. 31A. However, the modified depth surface 3160 includes lowalpha sections 3165 in the sections of the depth surface 3160representing discontinuities in the associated depth map. As describedearlier, a depth surface 3160 can be rendered with a corresponding alphachannel to indicate the quality of the depth surface 3160 at a givenpoint (or to aid in transitions between different depth surfaces).

In the embodiment of FIG. 31B, when the modified depth surface 3160 isrendered from the render viewpoint 3110 (still at a different angle 3115than the camera 3105 viewpoint) discrepancies still occur between therendering of the modified depth surface 3160 and the actual scenecomprising the obstructing and background objects 3120 and 3125.However, in the case of the modified depth surface 3160, the low alphasections 3165 of the modified depth surface comprise the areas where thediscrepancies will occur. For example, at the low alpha intersection3145 the modified depth surface 3160 is rendered with a low alpha value.As a result, if an additional depth surface having a view of the correctrendering point 3130 exists, because the low alpha section 3165 reducesthe alpha blending weight of the rendered modified depth surface 3160 atthat point, the additional view comparatively has a higher weight tocorrectly reflect rendering point 3130.

In some embodiments, discontinuities in a depth map can be detectedbased on the magnitude of the gradient of the depth map exceeding athreshold value, based on the difference in depth estimation between apixel and a neighboring pixel exceeding a threshold value, or any othersuitable method to detect abrupt changes in the depth estimates of adepth map. Similarly, when a depth surface is generated for the givendepth map, sections or triangles of the modified depth surface 3160corresponding to the discontinuities can be assigned a low alpha valueso as to have a reduced weight if another depth surface has conflictingcolor information for that area of the render view.

In other embodiments, a depth surface is rendered as a disconnectedseries of sections associated, for example, with a single pixel of thereference image. FIG. 31C illustrates an example sectioned depthsurface, according to one embodiment. The environment of FIG. 31C onceagain includes the same camera 3105 and scene comprising the obstructingobject 3120 and background object 3125 as FIGS. 31A and B. However, theenvironment of FIG. 31C includes a sectioned depth surface 3170 renderedas a collection of discrete sections. For example, each section of thesectioned depth surface 3170 can represent a pixel of the associatedreference image. In some embodiments, each section of the sectioneddepth surface 3170 is rendered parallel (or near-parallel) to the imagesensor of the camera 3105. Similarly, a “billboard” method can be usedin which each section of the sectioned depth surface 3170 is renderedparallel (or near-parallel) to the image plane of the render viewpoint3110. As an example, the near-parallel rendering may tilt each sectiontowards the render viewpoint by up to a maximum angle, such as 25degrees. Rendering a sectioned depth surface 3170 can be relativelyexpensive in terms of number of triangles used in the depth surface, aseach pixel of the depth map can be represented by 2 triangles in thesectioned depth surface 3170. To reduce the number of renderedtriangles, neighboring sections of the sectioned depth surface 3170 canbe joined or combined together to form a joined section 3180 based onthe neighboring sections being close in orientation and size.

Due to the gaps between sections, the sectioned depth surface 3170 haslarge spaces between neighboring sections of the depth surface withlarge differences in the depth estimates of the corresponding pixels ofthe reference image. Therefore, discontinuities in the depth map are notrendered in the section depth surface 3170, as the sectioned depthsurface 3170 is not rendered continuously. For example, where theoriginal depth surface 3175 would intersect be rendered at the previousintersection point 3145, instead there is a gap in the sectioned depthsurface 3170.

According to some embodiments, the sectioning of a sectioned depthsurface can result in render view artifacts when rendered from aviewpoint not aligned with the camera viewpoint associated with thedepth surface. FIG. 32A illustrates an example situation in which asectioned depth surface is rendered from a different angle, according toone embodiment. In the embodiment of FIG. 32A the sectioned depthsurface 3210 associated with the camera 3205 is rendered from the renderviewpoint 3220. In this example, the camera 3205 viewpoint (i.e. thenatural viewpoint of the sectioned depth map 3210) is different in anglefrom the render viewpoint 3220 and may result in gaps in view betweensections of the sectioned depth surfaces. In this example, the sectioneddepth surface 3210 does not have any discontinuities or other sharpchanges in depth estimations, and the sectioned depth surface 3210 canbe assumed to represent a continuous depth map of a single object orsurface. The difference in viewpoint between the camera 3205 viewpointand the render viewpoint 3220 can indicate that the render view from therender viewpoint 3220 should be similar to the reference image used togenerate the sectioned depth surface 3210.

The render viewpoint 3220 is associated with a series of depth rays3230. In an implementation using ray tracing methods to render, thedepth rays 3230 can represent rays used to determine pixels of therender view. As expected, some of the depth rays 3230 intersect with thesectioned depth surface 3210, for example at the intersection point 3245in this example. However, a set of non-intersecting rays 3240 do notintersect with the sectioned depth surface 3210, for example resultingin ray tracing rays that do not intersect the depth surface, resultingin gaps in the rendered sectioned depth surface 3210, according to someembodiments.

To reduce or eliminate gaps between depth surface sections in suchviewing angles, each section of the sectioned depth surface 3210 can beextended with neighbor color information, according to some embodiments.FIG. 32B illustrates an example situation in which an extended sectioneddepth surface is rendered from a different angle, according to oneembodiment. In the environment of FIG. 32B, the same sectioned depthsurface 3210 associated with the camera 3205 is rendered from the samerender viewpoint 3220. However, each section of the sectioned depthsurface 3210 has been extended by a predetermined amount, for example50% or 25% of the previous width of a section. Each extended section3250 comprises the color information of the neighboring section withwhich it overlaps (therefore maintaining direct view consistency) andcan serve as an additional surface for depth rays 3230 to intersect (orto be rendered by any other suitable method). In some embodiments, theextended sections 3250 are created by expanding the triangles alreadyforming each section of the sectioned depth surface 3210, and thus usingno extra triangles for rendering. Due to the extended sections 3250, thedepth rays 3230 continue to intersect with the sectioned depth surface3210 at the previous intersection points 3245, but also at additionalintersection points 3260. In some implementations, the use of extendedsections 3250 can reduce gaps or other artifacts present when renderinga sectioned depth surface 3210 from a slight off angle.

As mentioned previously, render views can be generated in any suitablefield of view or projection. In some implementations, an equirectangularprojection is used to generate one or more render views (hereinafter, arender view using an equirectangular projection will be referred to asan “equirect view”). In some cases, an equirect view is a monoscopic 360degree image of the scene as viewed from a single origin point (therender viewpoint). However, in other embodiments, equirect views areused in stereoscopic pairs (one equirect view for each eye of a user) togenerate a 3D 360 image which can be later displayed using a HIVID orother suitable viewing device. In a stereoscopic pair, the viewpoint ofa user's eye when turning in a 360 degree circle does not remain in astatic location, instead the user's eye viewpoint moves in a circle witha diameter of the user's interpupillary distance (“IPD”) as the userrotates through 360 degrees. Therefore, the process of rendering anequirect view can be adapted to approximate the correct viewpoint for auser's eye at each angle of the equirect view. In implementations usingray tracing methods for rendering, the changing viewpoint can beaccounted for by altering the ray origin of each ray appropriately.However, in embodiments using other rendering methods (for example,forward splatting or triangle rasterization methods) the renderingprocess can be adapted to render an equirect view with a changingviewpoint. For example, each triangle of the depth surfaces used torender the equirect view can be initially rendered based on the originpoint as normal, but then shifted to approximate the correct location ofthat triangle when viewed from the correct viewpoint for that specificangle of the equirect view. In some implementations, an equirect view isrendered using a single viewpoint (for example, ray tracing methods),but other implementations (for example, certain forward splatting ortriangle rasterization implementations) can render a cubemap from a setof intermediate images (for example, images representing the top,bottom, and sides of a cube) which are assembled to approximate theequirect view. According to some embodiments, rendering a cubemap for aequirect view with a changing viewpoint can be similarly adapted toadjust for the correct viewpoint.

FIG. 33 illustrates rendering a triangle for a render view using anequirectangular projection, according to one embodiment. The example ofFIG. 33 comprises an origin point 3310 for the equirect view and an IPDcircle 3320 with diameter equal to the IPD 3315 centered on the originpoint 3310. In some embodiments, the IPD circle 3320 represents the setof approximate viewpoints for each angle of the equirect view. Thecorrect viewpoint for any given angle is the tangent point 3330 of atangent line at that angle, according to some embodiments. In this case,there are two possible tangent lines for any given angle 3360; thecorrect tangent point 3330 can be determined based on if the left orright eye viewpoint is desired.

To render a triangle, for example the initial triangle 3340, thetriangle is first rendered as if the viewpoint was the origin point.Then a tangent line 3335 is drawn from the location of that triangle(here, the initial triangle location 3342) to the IPD circle 3320. Theresulting tangent point 3330 is the approximate viewpoint for thistriangle. Then, the initial triangle is shifted 3350 to approximate thecorrect viewpoint. In some embodiments, the initial triangle 3340 isshifted by an amount equal to half the IPD 3315 in a directionperpendicular to the tangent line 3335. This shift 3355 can maintain thesame angle 3360 between the initial triangle 3340 and the determinedviewpoint (the tangent point 3330) and between the shifted triangle 3345and the origin point 3310. In situations where an opposite side view isneeded, the opposite tangent point to the IPD circle 3320 is chosen. Forexample, in this example, the opposite would be roughly opposite thetangent point 3330 and would result in a shift of the initial triangle3340 generally upwards.

FIG. 34 is a flowchart outlining an example process for generating arender view based on a set of depth surfaces, according to oneembodiment. The process of FIG. 34 begins when a render viewpoint 3410is selected. The rendering module can the determine 3415 the set ofdepth surfaces needed to generate the desired render view. A depthsurface is then selected 3420 and rendered 3430 from the renderviewpoint by any suitable method. At this point any alpha values can beapplied to the rendered depth surface 3450, or, for example, therendered depth surface can be added to an accumulation view based on thealpha values of the depth surface. If all depth surfaces have beenrendered, all the rendered depth surfaces are combined to form the finalrender view 3470, but if additional depth surfaces remain, the processresumes from the step 3420.

CONCLUSION

The foregoing description of the embodiments of the invention has beenpresented for the purpose of illustration; it is not intended to beexhaustive or to limit the invention to the precise forms disclosed.Persons skilled in the relevant art can appreciate that manymodifications and variations are possible in light of the abovedisclosure.

Some portions of this description describe the embodiments of theinvention in terms of algorithms and symbolic representations ofoperations on information. These algorithmic descriptions andrepresentations are commonly used by those skilled in the dataprocessing arts to convey the substance of their work effectively toothers skilled in the art. These operations, while describedfunctionally, computationally, or logically, are understood to beimplemented by computer programs or equivalent electrical circuits,microcode, or the like. Furthermore, it has also proven convenient attimes, to refer to these arrangements of operations as modules, withoutloss of generality. The described operations and their associatedmodules may be embodied in software, firmware, hardware, or anycombinations thereof.

Any of the steps, operations, or processes described herein may beperformed or implemented with one or more hardware or software modules,alone or in combination with other devices. In one embodiment, asoftware module is implemented with a computer program productcomprising a computer-readable medium containing computer program code,which can be executed by a computer processor for performing any or allof the steps, operations, or processes described.

Embodiments of the invention may also relate to an apparatus forperforming the operations herein. This apparatus may be speciallyconstructed for the required purposes, and/or it may comprise ageneral-purpose computing device selectively activated or reconfiguredby a computer program stored in the computer. Such a computer programmay be stored in a non-transitory, tangible computer readable storagemedium, or any type of media suitable for storing electronicinstructions, which may be coupled to a computer system bus.Furthermore, any computing systems referred to in the specification mayinclude a single processor or may be architectures employing multipleprocessor designs for increased computing capability.

Embodiments of the invention may also relate to a product that isproduced by a computing process described herein. Such a product maycomprise information resulting from a computing process, where theinformation is stored on a non-transitory, tangible computer readablestorage medium and may include any embodiment of a computer programproduct or other data combination described herein.

Finally, the language used in the specification has been principallyselected for readability and instructional purposes, and it may not havebeen selected to delineate or circumscribe the inventive subject matter.It is therefore intended that the scope of the invention be limited notby this detailed description, but rather by any claims that issue on anapplication based hereon. Accordingly, the disclosure of the embodimentsof the invention is intended to be illustrative, but not limiting, ofthe scope of the invention, which is set forth in the following claims.

What is claimed is:
 1. A method comprising: identifying positioninginformation for each camera in a set of cameras, each camera having aposition with respect to an image capture system, an orientation, and anangle of view; determining a semi-random set of test points external tothe image capture system; initializing a plurality of candidate cameraorientation configurations, each camera orientation configurationcomprising an orientation of each of the cameras in the set of cameras,each orientation determining a field of view of an environment for thecamera based on the camera angle of view and position; for each of thecandidate camera orientation configurations: determining, for each testpoint of the set of test points, a number of cameras that view the testpoint in the camera field of view based on the angle of view, position,and orientation of each camera in the candidate camera orientationconfiguration; determining a minimum number of cameras that view anytest point in the camera field of view based on the number of camerasthat view the test points in set of test points; calculating, for thecandidate camera orientation configuration, a coverage score based onthe minimum number of cameras that view any test point; and modifyingthe orientation of one or more of the cameras in the candidate cameraorientation configuration to improve the coverage score for thecandidate camera orientation configuration; evaluating each of thecamera orientation configurations based on a second set of evenlydistributed test points; selecting a camera orientation configurationfrom the set of candidate camera orientation configurations based on theevaluating; and orienting one or more cameras of the set of camerasbased on the selected camera orientation configuration.
 2. The method ofclaim 1, wherein the positioning information for each camera isgenerated based on the solution to a Thomson problem for the set ofcameras.
 3. The method of claim 1, wherein determining a semi-random setof test points comprises: generating a random set of test points;evaluating the closeness of each test point in the random set of testpoints to the other test points of the random set of test points;discarding the test points closest to the other test points in therandom set of test points; and re-generating replacement test points forthe discarded test points.
 4. The method of claim 1, wherein modifyingthe orientation of one or more of the cameras in the candidate cameraorientation configuration comprises: modeling the field of view of eachcamera in the candidate camera orientation configuration as having adifferentiable transition function from a center of the field of view toan edge of the field of view.
 5. The method of claim 1, whereinmodifying the orientation of one or more of the cameras in the candidatecamera orientation configuration comprises: evaluating the optimizationof a candidate camera orientation configuration based on a secondarycoverage score reflecting a percentage of the set of test points havingmore than the determined minimum number of cameras that can view thetest point.
 6. The method of claim 1, wherein the second set of evenlydistributed test points is generated by a mathematical function.
 7. Themethod of claim 6, wherein the mathematical function is a Fibonaccispiral.
 8. The method of claim 1, further comprising assigning eachcamera of the set of cameras a coverage function modeling the field ofview of the camera.
 9. The method of claim 8, wherein modifying theorientation of one or more of the cameras in the candidate cameraorientation configuration to improve the coverage score for thecandidate camera orientation configuration comprises using an iterativesolving method to maximize the coverage score based on the coveragefunctions of each camera of the set of cameras.
 10. The method of claim8, wherein each coverage function is a differentiable sigmoid function.11. A non-transitory computer readable storage medium comprisinginstructions which, when executed by a processor, cause the processor toperform the steps of: identifying positioning information for eachcamera in a set of cameras, each camera having a position with respectto an image capture system, an orientation, and an angle of view;determining a semi-random set of test points external to the imagecapture system; initializing a plurality of candidate camera orientationconfigurations, each camera orientation configuration comprising anorientation of each of the cameras in the set of cameras, eachorientation determining a field of view of an environment for the camerabased on the camera angle of view and position; for each of thecandidate camera orientation configurations: determining, for each testpoint of the set of test points, a number of cameras that view the testpoint in the camera field of view based on the angle of view, position,and orientation of each camera in the candidate camera orientationconfiguration; determining a minimum number of cameras that view anytest point in the camera field of view based on the number of camerasthat view the test points in set of test points; calculating, for thecandidate camera orientation configuration, a coverage score based onthe minimum number of cameras that view any test point; and modifyingthe orientation of one or more of the cameras in the candidate cameraorientation configuration to improve the coverage score for thecandidate camera orientation configuration; evaluating each of thecamera orientation configurations based on a second set of evenlydistributed test points; selecting a camera orientation configurationfrom the set of candidate camera orientation configurations based on theevaluating; and orienting one or more cameras of the set of camerasbased on the selected camera orientation configuration.
 12. Thenon-transitory computer readable storage medium method of claim 11,wherein the positioning information for each camera is generated basedon the solution to a Thomson problem for the set of cameras.
 13. Thenon-transitory computer readable storage medium method of claim 11,wherein determining a semi-random set of test points comprises:generating a random set of test points; evaluating the closeness of eachtest point in the random set of test points to the other test points ofthe random set of test points; discarding the test points closest to theother test points in the random set of test points; and re-generatingreplacement test points for the discarded test points.
 14. Thenon-transitory computer readable storage medium method of claim 11,wherein modifying the orientation of one or more of the cameras in thecandidate camera orientation configuration comprises: modeling the fieldof view of each camera in the candidate camera orientation configurationas having a differentiable transition function from a center of thefield of view to an edge of the field of view.
 15. The non-transitorycomputer readable storage medium method of claim 11, wherein modifyingthe orientation of one or more of the cameras in the candidate cameraorientation configuration comprises: evaluating the optimization of acandidate camera orientation configuration based on a secondary coveragescore reflecting a percentage of the set of test points having more thanthe determined minimum number of cameras that can view the test point.16. The non-transitory computer readable storage medium method of claim11, wherein the second set of evenly distributed test points isgenerated by a mathematical function.
 17. The non-transitory computerreadable storage medium method of claim 16, wherein the mathematicalfunction is a Fibonacci spiral.
 18. The non-transitory computer readablestorage medium method of claim 11, further comprising assigning eachcamera of the set of cameras a coverage function modeling the field ofview of the camera.
 19. The non-transitory computer readable storagemedium method of claim 18, wherein modifying the orientation of one ormore of the cameras in the candidate camera orientation configuration toimprove the coverage score for the candidate camera orientationconfiguration comprises using an iterative solving method to maximizethe coverage score based on the coverage functions of each camera of theset of cameras.
 20. The non-transitory computer readable storage mediummethod of claim 18, wherein each coverage function is a differentiablesigmoid function.